Mastering Physics Solutions Chapter 4 Two-Dimensional Kinematics
Chapter 4 Two-Dimensional Kinematics Q.1CQ
What is the acceleration of a projectile when it reaches its highest point? What is its acceleration just before and just after reaching this point?
Solution:
Projectile motion, ignoring air resistance, always acts downward. Thus, during the entire motion projectile, acceleration remains constant.
Chapter 4 Two-Dimensional Kinematics Q.1P
CE Predict/Explain As you walk briskly down the street, you toss a small ball into the air. (a) If you want the ball to land in your hand when it comes back down, should you toss the ball straight upward, in a forward direction, or in a backward direction, relative to your body?
(b) Choose the best explanation from among the following:
I. If the ball is thrown straight up you will leave it behind.
II. You have to throw the ball in the direction you are walking.
III. The ball moves in the forward direction with your walking speed at all times.
Solution:
(a) If you want the ball to land in your hand when it comes back down, you should toss the ball straight upward.
(b) When a person tosses a ball upward while walking, the horizontal component of velocity of the ball and the person will be the same. So the ball moves in the forward direction with your walking speed at all times when you toss the ball straight upwards.
Therefore option III is correct.
Chapter 4 Two-Dimensional Kinematics Q.2CQ
A projectile is launched with an initial speed of v0 at an angle θ above the horizontal. It lands at the same level from which it was launched. What was its average velocity between launch and landing? Explain.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.2P
A sailboat runs before the wind with a constant speed of 4.2 m/s in a direction 32° north of west. How far (a) west and (b) north has the sailboat traveled in 25 min?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.3CQ
A projectile is launched from level ground. When it Sands, its direction of motion has rotated clockwise through 60°. What was the launch angle? Explain.
Solution:
The projectile was launched at an angle of 30°, so its direction of motion has rotated through 60º.
Chapter 4 Two-Dimensional Kinematics Q.3P
As you walk to class with a constant speed of 1.75 m/s, you are moving in a direction that is 18.0° north of east. How much time does it take to change your displacement by (a) 20.0 m east or (b) 30.0 m north?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.4CQ
In a game of baseball, a player hits a high fly ball to the outfield. (a) Is there a point during the flight of the ball where its velocity is parallel to its acceleration? (b) Is there a point where the ball’s velocity is perpendicular to its acceleration? Explain in each case.
Solution:
(a) No, the velocity has two components. The vertical component is tangential to the flight, and the horizontal component is always to the right. Velocity is not parallel to the acceleration in this case.
(b) The ball’s velocity is perpendicular to its acceleration when it is at maximum height.
Chapter 4 Two-Dimensional Kinematics Q.4P
Starting from rest, a car accelerates at 2.0 m/s2 up a hill that is inclined 5.5° above the horizontal, How far (a) horizontally and (b) vertically has the car traveled in 12 s?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.5CQ
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Chapter 4 Two-Dimensional Kinematics Q.5P
IP A particle passes through the origin with avelocity of (6.2m/s)ŷ. If the particle’s acceleration is (-4.4m/s2) , (a) what are its x and y positions after 5.0 s? (b) What are vx and uy at this time? (c) Docs the speed of this particle increase with time, decrease with time, or increase and then decrease? Explain.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.6CQ
Solution:
Chapter 4 Two-Dimensional Kinematics Q.6P
An electron in a cathode-ray tube is traveling horizontally at 2.10 × 109 cm/s when deflection plates give it an upward acceleration of 5.30 × 1017 cm/s2. (a) How long does it take for the electron to cover a horizontal distance of 6.20 cm? (b) What is its vertical displacement during this time?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.7CQ
Do projectiles for which air resistance is nonnegligible, such as a bullet fired from a rifle, have maximum range when the launch angle is greater than, less than, or equal to 45°? Explain.
Solution:
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Chapter 4 Two-Dimensional Kinematics Q.7P
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Chapter 4 Two-Dimensional Kinematics Q.8CQ
Two projectiles are launched from the same point at the same angle above the horizontal. Projectile 1 reaches a maximum height twice that of projectile 2. What is the ra tio of the initial speed of projectile 1 to the initial speed of projectile 2? Explain.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.8P
CE Predict/Explain Two divers run horizontally off the edge of a low cliff. Diver 2 runs with twice the speed of diver 1. (a) When the divers hit the water, is the horizontal distance covered by diver 2 twice as much, four times as much, or equal to the horizontal distance covered by diver 1? (b) Choose the best explanation from among the following:
I. The drop time is the same for both divers.
II. Drop distance depends on t2.
III. All divers in free fall cover the same distance.
Solution:
(a) The distance horizontal covered by the diver 2 is twice the horizontal distance covered by the diver 1.
(b) As the vertical distance traveled by the two divers is same, also both the divers has zero initial vertical component of velocity, therefore the time of travel for both the divers is same. Therefore diver 2 travels more time than the diver 1.
So option I is correct.
Chapter 4 Two-Dimensional Kinematics Q.9CQ
A child rides on a pony walking with constant velocity. The boy leans over to one side and a scoop of ice cream falls from his ice cream cone. Describe the path of the scoop of ice cream as seen by (a) the child and (b) his parents standing on the ground nearby.
Solution:
(A) The child sees the scoop falling straight downward.
(B) However, the father sees from the ground, that the trajectory of path of scoop is parabolic.
Chapter 4 Two-Dimensional Kinematics Q.9P
CE Predict/Explain Two youngsters dive off an overhang into a lake. Diver 1 drops straight down, and diver 2 runs off the cliff with an initial horizontal speed v0.(a) is the splashdown speed of diver 2 greater than, less than, or equal to the splashdown speed of diver 1? (b) Choose the best explanation from among the following:
I. Both divers are in free fall, and hence they will have the same splashdown speed.
II. The divers have the same vertical speed at splashdown, but diver 2 has the greater horizontal speed.
III. The diver who drops straight down gains more speed than the one who moves horizontally.
Solution:
(a) The splashdown speed of diver 2 is greater than the splash down speed of diver 1.
(b) The divers have same vertical speed at splashdown, but diver 2 has the greater horizontal speed. Therefore the diver 2 has the greater speed than the diver 1.
Therefore option II is the best.
Chapter 4 Two-Dimensional Kinematics Q.10CQ
Drivingdown the highway, you find yourself behind a heavily loaded tomato truck. You follow close behind the truck, keeping the same speed. Suddenly a tomato falls from the back of the truck. Will the tomato hit your car or land on the road, assuming you continue moving with the same speed and direction? Explain.
Solution:
When a tomato suddenly falls from the truck, it will land on the road because the horizontal speed is the same during the entire duration of the fall.
Chapter 4 Two-Dimensional Kinematics Q.10P
An archer shoots an arrow horizontally at a target 15 m away. The arrow is aimed directly at the center of the target, but it hits 52 cm lower. What was the initial speed of the arrow?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.11CQ
A projectile is launched from the origin of a coordinate system where the positive x axis points horizontally to the right and the positive y axis points vertically upward. What was the projectile’s launch angle with respect to the x axis if, at its highest point, its direction of motion has rotated (a) clockwise through 50° or (b) counterclockwise through 30°? Explain.
Solution:
(A) At the highest point, only the horizontal velocity exists. So it is launched from 50º to the positive x-axis.
(B) It is launched from 30º below the negative x-axis.
Chapter 4 Two-Dimensional Kinematics Q.11P
Victoria Falls The great, gray-green, greasy Zambezi River flows over Victoria Falls in south central Africa. The falls are approximately 108 m high. If the river is flowing horizontally at 3.60 m/s just before going over the falls, what is the speed of the water when it hitsthe bottom? Assume the water is in free fall as it drops.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.12P
A diver runs horizontally off the end of a diving board wi th an initial speed of 1.85 m/s. if the diving board is 3.00 m above the water, what is the diver’s speed just before she enters the water?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.13P
An astronaut on the planet Zircon tosses a rock horizontally with a speed of 6.95 m/s. The rock falls through a vertical distance of 1.40 m and lands a horizontal distance of 8.75 m from the astronaut. What is the acceleration of gravity on Zircon?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.14P
IP Pitcher’s Mounds Pitcher’s mounds are raised to compensate for the vertical drop of the ball as it travels a horizontal distance of 18 hi to the catcher, (a) If a pitch is thrown horizontally with an initial speed of 32 m/s, how far does it drop by the time it reaches the catcher? (b) If the speed of the pitch is increased, does the drop distance increase, decrease, or stay the same? Explain, (c) If this baseball game were to be played on the Moon, would the drop distance increase, decrease, or stay the same? Explain.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.15P
Solution:
Chapter 4 Two-Dimensional Kinematics Q.16P
Solution:
(C) The speed of the clam increases horizontally. However, the vertical velocity won’t change since only g and the time are counted in order to determine y.
Chapter 4 Two-Dimensional Kinematics Q.17P
Amountain climber jumpsa 2.8-m-wide crevasse by leaping horizontally with a speed of 7.8 m/s. (a) If the climber’s direction of motion on landing is -45°, what is the height difference between the two sides of the crevasse? (b) Where does the climber land?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.18P
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Chapter 4 Two-Dimensional Kinematics Q.19P
IP A white-crowned sparrow flying horizontally with a speed of 1.80 m/s folds its wings and begins to drop in free fall, (a) How far does the sparrow fall after traveling a horizontal distance of 0.500 m? (b) If the sparrow’s initial speed is increased, does the distance of fall increase, decrease, or stay the same?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.20P
If, in the previous problem, a jack-o-lantern is given an initial horizontal speed of 3.3 m/s, what are the direction and magnitude of its velocity (a) 0.75 s later, and (b) just before it lands?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.21P
Fairgoers ride a Ferris wheel with a radius of 5.00 m (Figure 4-16). The wheel completes one revolution every 32.0 s. (a) What is the average speed of a rider on this Ferris wheel? (b) If a rider accidentally drops a stuffed animal at the top of the wheel, where does it land relative to the base of the ride? (Note: The bottom of the wheel is 1.75 m above the ground.)
Solution:
Chapter 4 Two-Dimensional Kinematics Q.22P
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Chapter 4 Two-Dimensional Kinematics Q.23P
Baseball and the Washington Monument On August 25, 1894, Chicago catcher William Schriver caught a baseball thrown from the top of the Washington Monument (555 ft, 898 steps), (a) If the ball was thrown horizontally with a speed of 5.00 m/s, where did it land? (b) What were the ball’s speed and direction of motion when caught?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.24P
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Chapter 4 Two-Dimensional Kinematics Q.25P
IP A ball rolls off a table and falls 0.75 m to the floor, landing with a speed of 4.0 m/s. (a) What is the acceleration of the ball just before it strikes the ground? (b) What was the initial speed of the ball? (c) What initial speed must the ball have if it is to land with a speed of 5.0 m/s?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.26P
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Chapter 4 Two-Dimensional Kinematics Q.27P
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Chapter 4 Two-Dimensional Kinematics Q.28P
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Chapter 4 Two-Dimensional Kinematics Q.29P
A second baseman tosses the ball to the first baseman, who catches it at the same level from which it was thrown. The throw is made with an initial speed of 18.0 m/s at an angle of 37.5° above the horizontal, (a) What is the horizontal component of the ball’s velocity just before it is caught? (b) How long is the ball in the air?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.30P
Referring to the previous problem, what are the y component of the ball’s velocity and its direction of motion just before it is caught?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.31P
A cork shoots out of a champagne bottle at an angle of 35.0° above the horizontal. If the cork travels a horizontal distance of 1.30 m in 1.25s, what was its initial speed?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.32P
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Chapter 4 Two-Dimensional Kinematics Q.33P
In a game of basketball, a forward makes a bounce pass to the center. The ball is thrown with an initial speed of 4.3 m/s at an angle of 15° below the horizontal. Tt is released 0.80 m above the floor. What horizontal distance does the ball cover before bouncing?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.34P
Repeat the previous problem for a bounce pass in which the ball is thrown 15° above the horizontal.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.35P
IP Snowballs are thrown with a speed of 13 m/s from a roof 7.0 m above the ground. Snowball A is thrown straight down-
ward; snowball B is thrown in a direction 25° above the horizontal, (a) Is the landing speed of snowball A greater than, less than, or the same as the landing speed of snowball B? Explain. (b) Verify your answer to part (a) by calculating the landing speed of both snowballs.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.36P
In the previous problem, find the direction of motion of the two snowballs just before they land.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.37P
A golfer gives a ball a maximum initial speed of 34.4 m/s. (a) What is the longest possible hole-irt-one for this golfer? Neglect any distance the ball might roll on the green and assume that the tee and the green are at the same level, (b) What is the minimum speed of the ball during this hole-in-one shot?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.38P
What is the highest tree the ball in the previous problem could clear on its way to the longest possible holc-in-one?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.39P
The “hang time” of a punt is measured to be 4.50 s. If the ball was kicked at an angle of 63.0° above the horizontal and was caught at the same level from which it was kicked, what was its initial speed?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.40P
In a friendly game of handball, you hit the ball essentially at ground level and send it toward the wall with a speed of 18 m/s at an angle of 32° above the horizontal, (a) How long does it take for the ball to reach the wall if it is 3.8 m away? (b) How high is the ball when it hits the wall?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.41P
IP Tn the previous problem, (a) what are the magnitude and direction of the ball’s velocity when it stilkes the wall? (b) Has the ball reached the highest point of its trajectory at this time? Explain.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.42P
A passenger on the Ferris wheel described in Problem 21 drops his keys when he is on the way up and at the 10 o’clock position. Where do the keys land relative to thebase of the ride?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.43P
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Chapter 4 Two-Dimensional Kinematics Q.44P
A certain projectile is launched with an initial speed v0. At its highest point its speed is v0/4- What was the launch angle?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.45P
Punkin Chunkin In Sussex County, Delaware, a post-Halloween tradition is “Punkin Chunkin,” in which contestants build cannons, catapults, trebuchets, and other devices to launch pumpkins and compete for the greatest distance. Though hard to believe, pumpkins have been projected a distance of 4086 feet in this contest. What is the mnirmum initial speed needed for such a shot?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.46P
A dolphin jumps with an initial velocity of 12.0 m/s at an angle of 40.0° above the horizontal. The dolphin passes through the center of a hoop before returning to the water. If the dolphin is moving horizontally when it goes through the hoop, how high above the water is the center of the hoop?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.47P
A player passes a basketball to another player who catches it at the same level from which it was thrown. The initial speed of the ball is 7.1 m/s, and it travels a distance of 4.6 m. What were (a) the initial direction of the ball and (b) its time of flight?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.48P
A golf ball is struck with a five iron on level ground. It lands 92.2 m away 4.30 s later. What were (a) the direction and (b) the magnitude of the initial velocity?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.49P
A Record Toss Babe Didrikson holds the world record for the longest baseball throw (296 ft) by a woman. For the following questions, assume that the ball was thrown at an angle of 45.0° above the horizontal, that it traveled a horizontal distance of 296 ft, and that it was caught at the same level from which it was thrown, (a) What was the ball’s initial speed? (b) How long was the ball in the air?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.50P
In the photograph to the left on page 87, suppose the cart that launches the ball is 11 cm high. Estimate (a) the launch speed of the ball and (b) the time interval between successive stroboscopic exposures.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.51P
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Chapter 4 Two-Dimensional Kinematics Q.52P
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Chapter 4 Two-Dimensional Kinematics Q.53P
IP A soccer ball is kicked with an initial speed of 10.2 m/s in a direction 25.0° above the horizontal. Find the magnitude and direction of its velocity (a) 0.250 s and (b) 0.500 s after being kicked, (c) is the ball at its greatest height before or after 0.500 s? Explain.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.54P
A second soccer ball is kicked with the same initial speed as in Problem 53. After 0.750 s it is at its highest point. What was its initial direction of motion?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.55P
IP A golfer tees off on level ground, giving the ball an initial speed of 46.5 m/s and an initial direction of 37.5° above the horizontal, (a) How far from the golfer does the ball land? (b) The next golfer in the group hits a ball with the same initial speed but at an angle above the horizontal that is greater than 45.0°. Tf the second ball travels the same horizontal distance as the first ball, what was its initial direction of motion? Explain.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.56P
IP One of the most popular events at Highland games is the hay toss, where competitors use a pitchfork to throw a bale of hay over a raised bar. Suppose the initial velocity of a bale of hay is . (a) After what minimum time is its speed equal to 5,00 m/s? (b) How long after the hay is tossed is it moving in a direction that is 45.0° below the horizontal? (c) If the bale of hay is tossed with the same initial speed, only this time straight upward, will its time in the air increase, decrease, or stay the same? Explain.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.57GP
CE Child 1 throws a snowball horizontally from the top of a roof; child 2 throws a snowball straight down. Once in flight, is the acceleration of snowball 2 greater than, less than, or equal to the acceleration of snowball 1?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.58GP
Solution:
The penguin lands at an elevation that is above the water then the speed of the penguin gets decreased before it lands on the ice.
For a projectile initial and final point will be on the same level therefore velocity remains the same where as in the case of penguins jump from water to ice levels are different the speed before it land on ice becomes less.
Chapter 4 Two-Dimensional Kinematics Q.59GP
CE Predict/Explain A person flips a coin into the air and it lands on the ground a few feet away, (a) If the person were to perform an identical coin flip on an elevator rising with constant speed, would the coin’s time of flight be greater than, less than, or equal to its time of flight when the person was at rest? (b) Choose the best explanation from among the following:
I. The floor of the elevator is moving upward, and hence it catches up with the coin in mid flight.
II. The coin has the same upward speed as the elevator when it is tossed, and the elevator’s speed doesn’t change during the coin’s flight.
III. The coin starts off with a greater upward speed because of the elevator, and hence it reaches a greater height.
Solution:
(a) The time of flight of the coin in the lift moving up with constant speed is same as the time of flight on ground.
(b) This is because of the coin has the same upward speed as the elevator when it is tossed, and the elevator’s speed doesn’t change during the coin’s flight.
So option II is the best explanation.
Chapter 4 Two-Dimensional Kinematics Q.60GP
CEPredict/Explain Suppose the elevator in the previous problem is rising with a constant upward acceleration, rather than constant velocity, (a) In this case, would the coin’s time of flight be greater than, less than, or equal to its time of flight when the person was at rest? (b) Choose the best explanation from among the following:
I. The coin has the same acceleration once it is tossed, whether the elevator accelerates or not.
II. The elevator’s upward speed increases during the coin’s flight, and hence it catches up with the coin at a greater height than before.
III. The coin’s downward acceleration is less than before because the elevator’s upward acceleration partially cancels it.
Solution:
(a) The time of flight of the coin in the lift moving up with constant acceleration is less than the time of flight on ground.
(b) In this case the coin will have greater acceleration relative to the floor of the elevator. Or the elevator’s upward speed increases during the coin’s flight, and hence it catches up with the coin at greater height than before. So, the option II is the best explanation.
Chapter 4 Two-Dimensional Kinematics Q.61GP
A train moving with constant velocity travels 1.70 m north in 12 s and an undetermined, distance to the west. The speed of the train is 32 m/s. (a) Find the direction of the train’s motion relative to north, (b) How far west has the train traveled in this time?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.62GP
Referring to Example 4-2, find (a) the x component and (b) the y component of the hummingbird’s velocity at the time t = 0.72 s. (c) What is the bird’s direction of travel at this time, relative to the positive x axis?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.63GP
A racket ball is struck in such a way that it leaves the racket with a speed of 4.87 m/s in the horizontal direction. When the ball hits the court, it is a horizontal distance of 1.95 m from the racket. Find the height of the racket ball when it left the racket.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.64GP
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Chapter 4 Two-Dimensional Kinematics Q.65GP
Repeat the previous problem, this time assuming that the balloon is descending with a speed of 2.00 m/s.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.66GP
IP A soccer ball is kicked from the ground with an initial speed of 14.0 m/s. After 0.275 s its speed is 12.9 m/s. (a) Give a strategy that will allow you to calculate the ball’s initial direction of motion, (b) Use your strategy to find the initial direction.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.67GP
Solution:
Chapter 4 Two-Dimensional Kinematics Q.68GP
When the dried-up seed pod of a scotch broom plant bursts open, it shoots out a seed with an initial velocity of 2.62 m/s at an angle of 60.5° above the horizontal. If the seed pod is 0.455 m above the ground, (a) bow long does it take for the seed to land? (b) What horizontal distance does it cover during its flight?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.69GP
Referring to Problem 68, a second seed shoots out from the pod with the same speed but with a direction of motion 30.0° below the horizontal, (a) How long does it take for the second seed to land? (b) What horizontal distance does it cover during its flight?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.70GP
A shot-putter throws the shot with an initial speed of 12.2 m/s from a height of 5.15 ft above the ground. What is the range of the shot if the launch angle is (a) 20.0°, (b) 30.0°, or (c) 40.0°?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.71GP
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Chapter 4 Two-Dimensional Kinematics Q.72GP
Aball thrown straight upward returns to its original level in 2.75 s. A second ball is thrown at an angle of 40.0° above the horizontal. What is the initial speed of the second ball if it also returns to its original level in 2.75 s?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.73GP
IP A cannon is placed at the bottom of a cliff 61.5 m high. If the cannon is fired straight upward, the cannonball just reaches the top of the cliff, (a) What is the initial speed of the cannonball? (b) Suppose a second cannon is placed at the top of the cliff. This cannon is fired horizontally, giving its cannonbails the same initial speed found in part(a). Show that the range of this cannon is the same as the maximum range of the cannon at the base of the cliff. (Assume the ground at the base of the cliff is level, though the result is valid even if the ground is not level.)
Solution:
Chapter 4 Two-Dimensional Kinematics Q.74GP
IP A cannon is placed at the bottom of a cliff 61.5 m high. If the cannon is fired straight upward, the cannonball just reaches the top of the cliff, (a) What is the initial speed of the cannonball? (b) Suppose a second cannon is placed at the top of the cliff. This cannon is fired horizontally, giving its cannonbails the same initial speed found in part(a). Show that the range of this cannon is the same as the maximum range of the cannon at the base of the cliff. (Assume the ground at the base of the cliff is level, though the result is valid even if the ground is not level.)Solution:
Chapter 4 Two-Dimensional Kinematics Q.75GP
Sliot Put Record The men’s world record for the shot put, 23.12 in, was set by Randy Barnes of the United States on May 20,1990. If the shot was launched from 6.00 ft above the ground at an initial angle of 42.0°, what was its initial speed?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.76GP
Referring to Conceptual Checkpoint 4-3, suppose the two snowballs are thrown from an elevation of 15 m with an initial speed of 12 m/s. What is the speed of each ball when it is 5.0 m above the ground?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.77GP
IP A hockey puck just clears the 2.00-m-high boards on its way out of the rink. The base of the boards is 20.2 m from the pqint where the puck is launched, (a) Given the launch angle of the puck, θ, outline a strategy that you can use to find its initial speed, u0 (b) Use your strategy to find u0 for 0 = 15.0°.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.78GP
Referring to Active Example 4-2, suppose the ball is punted from an initial height of 0.750 m. What is the initial speed of the ball in this case?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.79GP
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Chapter 4 Two-Dimensional Kinematics Q.80GP
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Chapter 4 Two-Dimensional Kinematics Q.81GP
As discussed in Example 4-7, the archcrfish hunts by dislodging an unsuspecting insect from its resting place with a stream of water expelled from the fish’s mouth. Suppose the archerfish squirts water with a speed of 2.15 m/s at an angle of 52.0° above the horizontal, and aims for a beetle on a leaf 3.00 cm above the water’s surface, (a) At what horizontal distance from the beetle should the archerfish fire if it is to hit its target in the least time? (b) How much time will the beetle have to react?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.82GP
(a) What is the greatest horizontal distance from which the archerfish can hit the beetle, assuming the same squirt speed and direction as in Problem 81? (b) How much time docs the beetle have to react in this case?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.83GP
Find the launch angle for which the range and maximum height of a projectile are the same.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.84GP
A mountain climber jumps a crevasse of width W by leaping horizontally with speed u0.(a) if the height difference between the two sides of the crevasse is h, what is the minimum value of u0 for the climber to land safely on the other side? (b) In this case, what is the cumber’s direction of motion on landing?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.85GP
Prove that the landing speed of a projectile is independent of launch angle for a given height of launch.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.86GP
Solution:
Chapter 4 Two-Dimensional Kinematics Q.87GP
Landing on a Different Level A projectile fired from y = 0 with initial speed u0 e:\04-02-2016\chapter 4\1403\9781111788452\exercisesand initial angle θ lands on a different level, y = h. Show that the time of flight of the projectile is where T0 is the time of flight for h = 0 and H is the maximum height of the projectile.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.88GP
A mountain climber jumps a crevasse by leaping horizontally with speed u0. If the climber’s direction of motion on landing is θ below the horizontal, what is the height difference h between the two sides of the crevasse?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.89GP
Solution:
Chapter 4 Two-Dimensional Kinematics Q.90GP
Solution:
Chapter 4 Two-Dimensional Kinematics Q.91PP
Solution:
Chapter 4 Two-Dimensional Kinematics Q.92PP
How much time elapses between the first and second bounces?
A. 1.38 s
B. 2.58 s
C. 5.15 s
D. 5.33 s
Solution:
Chapter 4 Two-Dimensional Kinematics Q.93PP
How far does a rover travel in the horizontal direction between its first and second bounces?
A. 13.2 m
B. 49.4 m
C. 51.1m
D. 98.7 m
Solution:
Chapter 4 Two-Dimensional Kinematics Q.94PP
What is the average velocity of a rover between its first and second bounces?
A. 0
B. 2.57 m/s in the x direction
C. 9.92 m/s at 75.0° above the x axis
D. 9.58 m/s in the y direction
Solution:
Chapter 4 Two-Dimensional Kinematics Q.95IP
Referring to Example 4-5 (a) At what launch angle greater than 54.0° does the golf ball just barely miss the top of the tree in front of the green? Assume the ball has an initial speed of 13.5 m/s, and thatthe tree is 3.00 m high and is a horizontal distance of 14.0 m from the launch point, (b) Where does the ball land in the case described in part (a)? (c) At what launch angle less than 54.0° does the golf ball just barely miss the top of the tree in front of the green? (d) Where does the ball land in the case described in part (c)?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.96IP
Referring to Example 4-5 Suppose that the golf ball is launched with a speed of 15.0 m/s at an angle of 57.5° above the horizontal, and that it lands on a green 3.50 m above the level where it was struck, (a) What horizontal distance does the ball cover during its flight? (b) What increase in initial speed would be needed to increase the horizontal distance in part (a) by 7.50 m? Assume everything else remains the same.
Solution:
Chapter 4 Two-Dimensional Kinematics Q.97IP
Referring to Example 4-6 Suppose the ball is dropped at the horizontal distance of 5.50 m, but from a new height of 5.00 m. The dolphin jumps with the same speed of 12.0 m/s. (a) What launch angle must the dolphin have if it is to catch the ball? (b) At what height does the dolphin catch the ball in this case? (c) What is the minimum initial speed the dolphin must have to catch the ball before it hits the water?
Solution:
Chapter 4 Two-Dimensional Kinematics Q.98IP
IP Referring to Example 4-6 Suppose we change the dolphin’s launch angle to 45.0°, but everything else remains the same. Thus, the horizontal distance to the ball is 5.50 m, the drop height is 4.10 m, and the dolphin’s launch speed is 12.0 m/s. (a) What is the vertical distance between the dolphin and the ball when the dolphin reaches the horizontal position of the ball? We refer to this as the “miss distance.” (b) If the dolphin’s launch speed is reduced, will the miss distance increase, decrease, or stay the same? (c) Find the miss distance for a launch speed of 10.0 m/s.
Solution:
