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physics
mechanics
Physics 5th edition James S. Walker - Solutions
You walk in a straight line for 95 m at an angle of 162° above the positive x axis. What are the x and y components of your displacement?
Referring to Example 3-11,(a) What heading must the boat have if it is to land directly across the river from its starting point?(b) How much time is required for this trip if the river is 25.0 m wide?(c) Suppose the speed of the boat is increased, but it is still desired to land directly across
Vector A(vector) points in the negative x direction. Vector B(vector) points at an angle of 30.0° above the positive x axis. Vector C(vector) has a magnitude of 15 m and points in a direction 40.0° below the positive x axis. Given that A(vector) + B(vector) + C(vector) = 0, find the magnitudes of
As two boats approach the marina, the velocity of boat 1 relative to boat 2 is 2.15 m/s in a direction 47.0° east of north. If boat 1 has a velocity that is 0.775 m/s due north, what is the velocity (magnitude and direction) of boat 2?
What speed must the dragonfly have if the line of sight, which is parallel to the x axis initially, is to remain parallel to the x axis?A. 0.562 m/sB. 0.664 m/sC. 1.00 m/sD. 1.13 m/s
Suppose the dragonfly now approaches its prey along a path with θ > 48.5°, but it still keeps the line of sight parallel to the x axis. Is the speed of the dragonfly in this new case greater than, less than, or equal to its speed in Problem 83?
If the dragonfly approaches its prey with a speed of 0.950 m/s, what angle u is required to maintain a constant line of sight parallel to the x axis?A. 37.9°B. 38.3°C. 51.7°D. 52.1°
In a similar situation, the dragonfly is observed to fly at a constant speed, but its angle to the x axis gradually increases from 20° to 40°. Which of the following is the best explanation for this behavior?A. The prey is moving in the positive y direction and maintaining a constant speed.B. The
Suppose the speed of the boat relative to the water is 7.0 m/s.(a) At what angle to the x axis must the boat be headed if it is to land directly across the river from its starting position?(b) If the speed of the boat relative to the water is increased, will the angle needed to go directly across
Suppose that the boat has a speed of 6.7 m/s relative to the water, and that the dock on the opposite shore of the river is at the location x = 55 m and y = 28 m relative to the starting point of the boat.(a) At what angle relative to the x axis must the boat be pointed in order to reach the other
Find the x and y components of a position vector r̅ of magnitude r = 88 m, if its angle relative to the x axis is(a) 32.0°(b) 64.0°.
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.
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.
A projectile is launched from a level surface with an initial velocity of v(vector) = (2 m/s) x̂ + (4 m/s) ŷ. What is the velocity of the projectile just before it lands? Explain.
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 ratio of the initial speed of projectile 1 to the initial speed of projectile 2? 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
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 as, four times as much as, or equal to the horizontal distance covered by diver 1? (b) Choose the
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
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?
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 hits the bottom? Assume the water is in
A diver runs horizontally off the end of a diving board with 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?
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 due to gravity on Zircon?
Pitcher's mounds are raised to compensate for the vertical drop of the ball as it travels a horizontal distance of 18 m 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
Playing shortstop, you pick up a ground ball and throw it to second base. The ball is thrown horizontally, with a speed of 18 m/s, directly toward point A (FIGURE 4-19). When the ball reaches the second baseman 0.54 s later, it is caught at point B.(a) How far were you from the second baseman?(b)
A crow is flying horizontally with a constant speed of 2.70 m/s when it releases a clam from its beak (FIGURE 4-20). The clam lands on the rocky beach 2.10 s later. Just before the clam lands, what are(a) Its horizontal component of velocity,(b) Its vertical component of velocity?(c) How would your
A mountain climber jumps a 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?
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(b) North has the sailboat traveled in 25 min?
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
In Denver, children bring their old jack-o-lanterns to the top of a tower and compete for accuracy in hitting a target on the ground (FIGURE 4-21). Suppose that the tower is 9.0 m high and that the bull's-eye is a horizontal distance of 3.5 m from the launch point. If the pumpkin is thrown
Fairgoers ride a Ferris wheel with a radius of 5.00 m (FIGURE 4-22). 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
A swimmer runs horizontally off a diving board with a speed of 3.32 m/s and hits the water a horizontal distance of 1.78 m from the end of the board. (a) How high above the water was the diving board? (b) If the swimmer runs off the board with a reduced speed, does it take more, less, or the same
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?
A basketball is thrown horizontally with an initial speed of 4.20 m/s (FIGURE 4-23). A straight line drawn from the release point to the landing point makes an angle of 30.0° with the horizontal. What was the release height?
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?
A certain projectile is launched with an initial speed v0. At its highest point its speed is 1/2v0. What was the launch angle of the projectile?A. 30°B. 45°C. 60°D. 75°
Three projectiles (A, B, and C) are launched with the same initial speed but with different launch angles, as shown in FIGURE 4-24. Rank the projectiles in order of increasing(a) Horizontal component of initial velocity(b) Time of flight. Indicate ties where appropriate.
Three projectiles (A, B, and C) are launched with different initial speeds so that they reach the same maximum height, as shown in FIGURE 4-25. Rank the projectiles in order of increasing(a) Initial speed(b) Time of flight. Indicate ties where appropriate.
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 position by(a) 20.0 m east or(b) 30.0 m north?
A cannonball is launched at an angle above level ground, giving it an initial vertical and horizontal velocity that are each positive. The cannonball lands at a time T after it is launched.(a) Which plot (A, B, C, D, or E) in FIGURE 4-26 best represents the horizontal component of the cannonball's
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)
A soccer ball is kicked with a speed of 15.6 m/s at an angle of 32.5° above the horizontal. If the ball lands at the same level from which it was kicked, for what amount of time was it in the air?
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. It is released 0.80 m above the floor. What horizontal distance does the ball cover before bouncing?
Snowballs are thrown with a speed of 13 m/s from a roof 7.0 m above the ground. Snowball A is thrown straight downward; 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?
In Problem 34, find the direction of motion of the two snowballs just before they land. In problem Snowballs are thrown with a speed of 13 m/s from a roof 7.0 m above the ground. Snowball A is thrown straight downward; snowball B is thrown in a direction 25° above the horizontal.
A golfer gives a ball a maximum initial speed of 51.4 m/s. (a) What is the longest possible hole-in-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
What is the highest tree the ball in the previous problem could clear on its way to the longest possible hole-in-one?
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?
In a friendly game of handball, you hit the ball essentially at ground level and send it toward the wall with a speed of 16 m/s at an angle of 37° above the horizontal. (a) What amount of time is required for the ball to reach the wall if it is 3.3 m away? (b) How high is the ball when it hits the
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(b) Vertically has the car traveled in 12 s?
On a hot summer day, a young girl swings on a rope above the local swimming hole (FIGURE 4-27). When she lets go of the rope her initial velocity is 2.25 m/s at an angle of 35.0° above the horizontal. If she is in flight for 0.616 s, how high above the water was she when she let go of the rope?
A certain projectile is launched with an initial speed v0. At its highest point its speed is v0/4. What was the launch angle?
In Dover, 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 4694 feet in this contest.
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?
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 (b) Its time of flight?
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 (b) The magnitude of the initial velocity?
You throw a ball into the air with an initial speed of 10 m/s at an angle of 60° above the horizontal. The ball returns to the level from which it was thrown in the time T.(a) Referring to FIGURE 4-28, which of the plots (A, B, or C) best represents the speed of the ball as a function of
A football quarterback shows off his skill by throwing a pass 45.70 m downfield and into a bucket. The quarterback consistently launches the ball at 38.00° above horizontal, and the bucket is placed at the same level from which the ball is thrown. (a) What initial speed is needed so that the ball
A clever inventor has created a device that can launch water balloons with an initial speed of 85.0 m/s. Her goal is to pass a balloon through a small hoop mounted on the observation platform at the top of the Eiffel Tower, 276 m above the ground. If the balloon is to pass through the hoop at the
Astronomers have discovered several volcanoes on Io, a moon of Jupiter. One of them, named Loki, ejects lava to a maximum height of 2.00 × 105 m.(a) What is the initial speed of the lava? (The acceleration of gravity on Io is 1.80 m/s2.)(b) If this volcano were on Earth, would the maximum height
Predict/Calculate A particle passes through the origin with a velocity of (6.2 m/s) ŷ. If the particle's acceleration is (- 4.4 m/s2) x̂,(a) What are its x and y positions after 5.0 s?(b) What are vx and vy at this time?(c) Does the speed of this particle increase with time, decrease with time,
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(b) 0.500 s after being kicked.(c) Is the ball at its greatest height before or after 0.500 s? Explain.
A soccer ball is kicked with an initial speed of 8.25 m/s. After 0.750 s it is at its highest point. What was its initial direction of motion?
An archer shoots an arrow over a castle wall by launching it with an initial speed of 28 m/s at 65° above horizontal. Assume the arrow lands on the other side of the castle wall at the same elevation as the launch point. (a) What maximum height does the arrow attain? (b) What is the range of the
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?
The penguin to the left in the accompanying photo is about to land on an ice floe. Just before it lands, is its speed greater than, less than, or equal to its speed when it left the water?
Dolphins may leap from the water just for the fun of it. At the instant a leaping dolphin lands, is its speed greater than, less than, or equal to its speed when it left the water?
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
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
A train moving with constant velocity travels 170 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?
A tennis 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 tennis ball when it left the racket.
A skateboarder travels on a horizontal surface with an initial velocity of 3.8 m/s toward the south and a constant acceleration of 2.2 m/s2 toward the east. Let the x direction be eastward and the y direction be northward, and let the skateboarder be at the origin at t = 0.(a) What are her x and y
A person tosses a ball for her puppy to retrieve. The ball leaves her hand horizontally with a speed of 4.6 m/s. If the initial height of the ball is 0.95 m above the ground, how far does it travel in the horizontal direction before landing?
An osprey flies horizontally with a constant speed of 6.8 m/s when it drops the fish it was carrying. How much time elapses after the fish is dropped before the speed of the fish doubles?
A hot-air balloon rises from the ground with a velocity of 12.00 m/s2ŷ. A champagne bottle is opened to celebrate takeoff, expelling the cork horizontally with a velocity of 15.00 m/s2 x̂ relative to the balloon. When opened, the bottle is 6.00 m above the ground.(a) What is the initial velocity
In a friendly neighborhood squirt gun contest a participant runs at 7.8 m/s horizontally off the back deck and fires her squirt gun in the plane of her motion but 45° above horizontal. The gun can shoot water at 11 m/s relative to the barrel, and she fires the gun 0.42 s after leaving the deck.(a)
An agitated llama may spit to assert dominance, or to ward off threats. Llamas can spit a considerable distance, and people handling them need to keep this in mind. If the spittle from a llama is launched from an initial height of 1.8 m with a speed of 6.1 m/s, and at an angle of 12° above
A particle leaves the origin with an initial velocity v(vector) = (2.40 m/s) x̂, and moves with constant acceleration a(vector) = (– 1.90 m/s2) x̂ + (3.20 m/s2) ŷ.(a) How far does the particle move in the x direction before turning around?(b) What is the particle's velocity at this time?(c)
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) What amount of time does it take for the seed to land?(b) What horizontal distance
In an Internet video an athlete launches a basketball from a stadium platform that is 16.2 m higher than the hoop. He makes the basket by launching the ball at an angle of 14.5° above horizontal with a speed of 11.6 m/s. What horizontal distance does the ball travel before passing through the hoop?
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°, (c) 40.0°?
Two marbles are launched at t = 0 in the experiment illustrated in FIGURE 4-29. Marble 1 is launched horizontally with a speed of 4.20 m/s from a height h = 0.950 m. Marble 2 is launched from ground level with a speed of 5.94 m/s at an angle θ = 45.0° above the horizontal.(a) Where would the
A hot-air balloon is drifting in level flight due east at 2.5 m/s due to a light wind. The pilot suddenly notices that the balloon must gain 24 m of altitude in order to clear the top of a hill 120 m to the east.(a) How much time does the pilot have to make the altitude change without crashing into
Coast Guard rescue swimmers are trained to leap from helicopters into the sea to save boaters in distress. The rescuers like to step off their helicopter when it is "ten and ten," which means that it is ten feet above the water and moving forward horizontally at ten knots. What are(a) The speed(b)
A football player kicks a field goal, launching the ball at an angle of 48° above the horizontal. During the kick, the ball is in contact with the player's foot for 0.045 s, and the ball's acceleration is 290 m/s2. What is the range of the football?
A ball 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?
To decide who pays for lunch, a passenger on a moving train tosses a coin straight upward with an initial speed of 5.25 m/s and catches it again when it returns to its initial level. From the point of view of the passenger, then, the coin's initial velocity is (5.25 m/s)ŷ. The train's velocity
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,
A golfer hits a shot to an elevated green. The ball leaves the club with an initial speed of 16 m/s at an angle of 58° above the horizontal. If the speed of the ball just before it lands is 12 m/s, what is the elevation of the green above the point where the ball is struck?
A men's world record for the shot put, 23.12 m, 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?
Referring to Conceptual Example 4-13, suppose the two cats jump from an elevation of 2.5 m with an initial speed of 3.0 m/s. What is the speed of each cat when it is 1.0 m above the ground?
A quarterback can throw a receiver a high, lazy "lob" pass or a low, quick "bullet" pass. These passes are indicated by curves 1 and 2, respectively, in FIGURE 4-30.(a) The lob pass is thrown with an initial speed of 21.5 m/s and its time of flight is 3.97 s. What is its launch angle?(b) The bullet
For summertime fun, you decide to combine diving from a board with shooting a basketball through a hoop.(a) During several practice runs you stand at the end of a diving board and launch the basketball horizontally from a position 4.50 m above the water. If the average landing spot is 6.25 m
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 much time does it take for the electron to cover a horizontal distance of 6.20 cm?(b) What is its vertical displacement during this
When the twin exploration rovers, Spirit and Opportunity, landed on Mars, their method of landing was unique and elaborate. After initial braking with rockets and parachutes to a virtual standstill several meters above the ground, the rovers inflated four air bags with six lobes each. The rovers
A useful rule of thumb in piloting is that if the heading from your airplane to a second airplane remains constant, the two airplanes are on a collision course. Consider the two airplanes shown in FIGURE 4-33. At time t = 0, airplane 1 is at the location (X, 0) and moving in the positive y
As discussed in Example 4-14, the archerfish 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
Find the launch angle for which the range and maximum height of a projectile are the same.
A mountain climber jumps a crevasse of width W by leaping horizontally with speed v0. (a) If the height difference between the two sides of the crevasse is h, what is the minimum value of v0 for the climber to land safely on the other side? (b) In this case, what is the climber's direction of
A projectile fired from y = 0 with initial speed v0 and initial angle u lands on a different level, y = h. Show that the time of flight of the projectile isIn this expression, T0 is the time of flight for h = 0, and H is the maximum height of the projectile.
A mountain climber jumps a crevasse by leaping horizontally with speed v0. If the climber's direction of motion on landing is u below the horizontal, what is the height difference h between the two sides of the crevasse?
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