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Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions

A stone is thrown vertically upward. On its way up it passes point A with speed v, and point B, 3.00 m higher than A, with speed ½ v. Calculate(a) The speed y and(b) The maximum height reached by the stone above point B.
A rock is dropped (from rest) from the top of a 60-m-tall building. How far above the ground is the rock 1.2s before it reaches the ground?
An iceboat has a constant velocity toward the east when a sudden gust of wind causes the iceboat to have a constant acceleration toward the east for a period of 3.0 s. A plot of x versus / is shown in Figure, where t = 0 is taken to be the instant the wind starts to blow and the positive x axis is
A ball is thrown vertically downward from the top of a36.6-m-tall building. The ball passes the top of a window that is 12.2 m above the ground 2.00 s after being thrown. What is the speed of the ball as it passes the top of the window?
The speed of a bullet is measured to be 640 m/s as the bullet emerges from a barrel of length 1.20 m, assuming constant acceleration, find the time that the bullet spends in the barrel after it is fired.
A parachutist bails out and freely falls 50 m. Then the parachute opens, and thereafter she decelerates at 2.0 m/s2. She reaches the ground with a speed of 3.0m/s. (a) How long is the parachutist in the air? (b) At what height does the fall begin?
The Zero Gravity Research Facility at the NASA Glenn Research Center includes a 145 m drop tower. This is an evacuated vertical tower through which, among other possibilities, a 1 m diameter sphere containing an experimental package can be dropped.(a) How long is the sphere in free fall?(b) What is
A ball is thrown down vertically with an initial speed of us from a height of h.(a) What is its speed just before it strikes the ground?(b) How long does the ball take to reach the ground? What would be the answers to?(c) Part a and(d) Part b if the ball were thrown upward from the same height and
A car can be braked to a stop from the autobahn-like speed of 200km/h in 170m, assuming the acceleration is constant, find its magnitude in (a) SI units and (b) In terms of g. (c) How much time Tb is required for the braking? Your reaction time Tr, is the time you require to perceive an emergency,
The sport with the fastest moving ball is jai alai, where measured speeds have reached 303km/h. If a professional jai alai player faces a ball at that speed and involuntarily blinks, he blacks out the scene for 100ms. How far does the ball move during the blackout?
Figure gives the path of a squirrel moving about on level ground, from point A (at time t = 0), to points B (at t = 5.00 min), C (at t =10.0 min), and finally D (at t = 15.0 min). Consider the average velocities of the squirrel from point A to each of the other three points. Of them, what are
The position vector r = 5.00ri + (et + ft2)j locates a particle as a function of time t. Vector r is in meters, t is in seconds, and factors e and f are constants. Figure gives the angle θ of the particle's direction of travel as a function of t θ is measured from the positive x direction). What
A proton initially has v = 4.0i – 2.0j + 3.0k and then 4 later has v = –2.0i – 2.0j + 5.0k (in meters per second). For that 4.0 s, what are?(a) The proton's average acceleration aavg in unit-vector notation,(b) The magnitude of aavg and(c) The angle between aavg and the positive direction of
The current world-record motorcycle jump is 77.0 m, set by Jason Renie. Assume that he left the take-off ramp at 12.0o to the horizontal and that the take-off and landing heights are the same. Neglecting air drag, determine his take-off speed.
A trebuchet was a hurling machine built to attack the walls of a castle under siege. A large stone could be hurled against a wall to break apart the wall. The machine was not placed near the wall because then arrows could reach it from the castle wall. Instead, it was positioned so that the stone
During a tennis match, a player serves the ball at 23.6 m/s, with the center of the ball leaving the racquet horizontally 2.37 m above the court surface. The net is 12 m away and 0.90 m high. When the ball reaches the net,(a) Does the ball clear it and(b) What is the distance between the center of
In a jump spike, a volleyball player slams the ball from overhead and toward the opposite floor. Controlling the angle of the spike is difficult. Suppose a ball is spiked from a height of 2.30 m with an initial speed of 20.0 m/s at a downward angle of 18.00o. How much farther on the opposite floor
Suppose that a shot putter can put a shot at the world-class speed v0 = 15.00 m/s and at a height of 2.160 m. What horizontal distance would the shot travel if the launch angle θ0 is?(a) 45.00o and(b) 42.00o? The answers indicate that the angle of 45o, which maximizes the range of projectile
In 1939 or 1940, Emanuel Zucchini took his human-cannonball act to an extreme: After being shot from a cannon, he soared over three Ferris wheels and into a net (Fig. 4.42) (a) Treating him as a particle, calculate his clearance over the first wheel. (b) If he reached maximum height over the middle
Upon spotting an insect on a twig overhanging water, an archer fish squirts water drops at the insect to knock it into the water (Figure). Although the fish sees the insect along a straight-line path at angle Ф and distance d, a drop must be launched at a different angle Ф0 if its parabolic path
In Sample Problem 4-7b, a ball is shot through a horizontal distance of 686 m by a cannon located at sea level and angled at 45o from the horizontal How much greater would the horizontal distance have been had the cannon been 30 m higher?
(a) If an electron is projected horizontally with a speed of 3.0 x 106 m/s, how far will it fall in traversing 1.0 m of horizontal distance?(b) Does the answer increase or decrease if the initial speed is increased?
The magnitude of the velocity of a projectile when it is at its maximum height above ground level is 10 m/s.(a) What is the magnitude of the velocity of the projectile 1.0 s before it achieves its maximum height?(b) What is the magnitude of the velocity of the projectile 1.0 s after it achieves its
A frightened rabbit moving at 6.0 m/s due east runs onto a large area of level ice of negligible friction. As the rabbit slides across the ice, the force of the wind causes it to have a constant acceleration of 1.4 m/s2, due north. Choose a coordinate system with the origin at the rabbit's initial
The pilot of an aircraft flies due east relative to the ground in a wind blowing 20 km/h toward the south. If the speed of the aircraft in the absence of wind is 70 km/h, what is the speed of the aircraft relative to the ground?
The pitcher in a slow-pitch softball game releases the ball at a point 3.0 ft above ground level. A stroboscopic plot of the position of the ball is shown in Figure, where the readings are 0.25 s apart and the ball is released at t = 0. (a) What is the initial speed of the ball? (b) What is the
The New Hampshire State Police use aircraft to enforce highway speed limits. Suppose that one of the airplanes has a speed of 135mi/h in still air. It is flying straight north so that it is at all times directly above a north-south highway. A ground observer tells the pilot by radio that a 10.0
The position r of a particle moving in the xy plane is given by r = 2ti + 2 sin [(π/4rad/s) t] j, where r is in meters and r is in seconds.(a) Calculate the x and y components of the particle's position at t = 0, 1.0, 2.0, 3.0, and 4.0 s and sketch the particle's path in the xy plane for the
A golfer tees off from the top of a rise, giving the golf ball an initial velocity of 43 m/s at an angle of 30° above the horizontal. The ball strikes the fairway a horizontal distance of 180 m from the tee. Assume the fairway is level.(a) How high is the rise above the fairway?(b) What is the
A track meet is held on a planet in a distant solar system. A shot-putter releases a shot at a point 2.0 m above ground level. A stroboscopic plot of the position of the shot is shown in Figure, where the readings are 0.50 s apart and the shot is released at time t = 0. (a) What is the initial
In basketball, hang is an illusion in which a player seems to weaken the gravitational acceleration while in midair. The illusion depends much on a skilled player's ability to rapidly shift the ball between hands during the flight, but it might also be supported by the longer horizontal distance
A skilled skier knows to jump upward before reaching a downward slope. Consider a jump in which the launch speed is v0 = 10m/s, the launch angle is θ0 = 9.0o, the initial course is approximately flat, and the steeper track has a slope of 11.3o. Figure 4-45a shows a pre-jump that allows the skier
A ball is to be shot from level ground with a certain speed. Figure shows the range R it will have versus the launch angle θ0. The value of θ0 determines the flight time; let tmax represent the maximum flight time. What is the least speed the ball will have during its flight if θ0 is chosen such
A ball rolls horizontally off the top of a stairway with a speed of 1 .52m/s. The steps are 20.3 cm high and 20.3 cm wide. Which step does the ball hit first?
Two seconds after being projected from ground level, a projectile is displaced 40 m horizontally and 53 m vertically above its launch point. What are the(a) Horizontal and(b) Vertical components of the initial velocity of the projectile?(c) At the instant the projectile achieves its maximum height
In Figure, a baseball is hit at a height h = 1.00m and then caught at the same height. It travels alongside a wall, moving up past the top of the wall 1.00 s after it is hit and then down past the top of the wall 4.00 s later, at distance D = 50.0 m farther along the wall. (a) What horizontal
A centripetal-acceleration addict rides in uniform circular motion with period T = 2.0s and radius r = 3.00m. At t1 his acceleration is a = (6.00 m/s2) i + (– 4.00 m/s2)j. At that instant, what are the values of(a) v ∙ a and(b) r x a?
A woman rides a carnival Ferris wheel at radius 1-5 m, completing five turns about its horizontal axis every minute. What are?(a) The period of the motion, the(b) Magnitude and(c) Direction of her centripetal acceleration at the highest point, and the(d) Magnitude and(e) Direction of her
What is the magnitude of the acceleration of a sprinter running at 10m/s when rounding a turn of a radius 25m?
When a large star becomes a supernova, its core may be compressed so tightly that it becomes a neutron star, with a radius of about 20 km (about the size of the San Francisco area). If a neutron star rotates once every second,(a) What is the speed of a particle on the star's equator and(b) What is
An Earth satellite moves in a circular orbit 640 km above Earth's surface with a period of 98.0 min. What are the(a) Speed and(b) Magnitude of the centripetal acceleration of the satellite?
A carnival merry-go-round rotates about a vertical axis at a constant rate. A man standing on the edge has a constant speed of 3.66 m/s and a centripetal acceleration d of magnitude 1.83 m/s2. Position vector r locates him relative to the rotation axis.(a) What is the magnitude of r? What is the
A rotating fan completes 1200 revolutions every minute. Consider the tip of a blade, at a radius of 0.15m.(a) Through what distance does the tip move in one revolution? What are?(b) The tip's speed and(c) The magnitude of its acceleration?(d) What is the period of the motion?
A purse at radius 2.00 m and a wallet at radius 3.00m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (2.00 m/s2) i + (4.00 m/s2)j. At that instant and in unit-vector notation,
A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 4.00s, it is at point (5.00 m, 6.00 m) with velocity (3.00 m/s)j and acceleration in the positive x direction. At time t2 = 10.0 s, it has velocity (– 3.00 m/s) i and acceleration in the
At t1 = 2.00 s, the acceleration of a particle in counterclockwise circular motion is (6.00 m/s2) i + (4.00 m/s2) j. It moves at constant speed. At time t2 = 5.00 s, its acceleration is (4.00 m/s2) i + (– 6.00 m/s2) j. What is the radius of the path taken by the particle if t2 – t1 is less than
A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.00 m, 4.00 m) with a velocity of -5.00i m/s and an acceleration of + 12.5j m/s2. What are the(a) x and(b) y coordinates of the center of the circular
A boy whirls a stone in a horizontal circle of radius 1.5m and at height 2.0 m above level ground. The string breaks, and the stone flies off horizontally and strikes the ground after traveling a horizontal distance of 10 m. What is the magnitude of the centripetal acceleration of the stone during
A cat rides a merry-go-round turning with uniform circular motion. At time t1 = 2.00 s, the cat's velocity is v1 = (3.00 m/s) i + (4.00 m/s) j, measured on a horizontal xy coordinate system. At t2 = 5.00 s, its velocity is v2 = (–3.00 m/s) i + (– 4.00 m/s) j . What are?(a) The magnitude of the
A cameraman on a pickup truck is traveling westward at 20 km/h while he videotapes a cheetah that is moving westward 30 km/h faster than the truck. Suddenly, the cheetah stops, turns, and then runs at 45 km/h eastward, as measured by u suddenly nervous crew member who stands alongside the cheetah's
A boat is traveling upstream in the positive direction of an x axis at 14 km/h with respect to the water of a river. The water is flowing at 9.0 km/h with respect to the ground. What are the(a) Magnitude and(b) Direction of the boat's velocity with respect to the ground? A child on the boat walks
A suspicious-looking man runs as fast as he can along a moving sidewalk from one end to the other, taking 2.50 s. Then security agents appear, and the man runs as fast as he can back along the sidewalk to his starting point, taking 10.0 s. What is the ratio of the man's running speed to the
A rugby player runs with the ball directly toward his opponent's goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball's velocity relative to the field does not have a positive x component. Suppose the player runs at speed 4.0 m/s relative
Two ships, A and B, leave port at the same time. Ship A travels northwest at 24 knots, and ship B travels at 28 knots in a direction 40o west of south. (1 knot = 1 nautical mile per hour; see Appendix D.) What are the(a) Magnitude and(b) Direction of the velocity of ship A relative to B?(c) After
A light plane attains airspeed of 500km/h. The pilot sets out for a destination 800 km due north but discovers that the plane must be headed 20.0" east of due north to fly there directly. The plane arrives in 2.00h. What were the(a) Magnitude and(b) Direction of the wind velocity?
Snow is falling vertically at a constant speed of 8.0m/s. At what angle from the vertical do the snowflakes appear to be falling as viewed by the driver of a car traveling on a straight, level road with a speed of 50 km/h?
After flying for 15 min in a wind blowing 42 km/h at an angle of 20o south of east, an airplane pilot is over a town that is 55 km due north of the starting point. What is the speed of the airplane relative to the air?
A train travels due south at 30 m/s (relative to the ground) in a rain that is blown toward the south by the wind. The path of each raindrop makes an angle of 70o with the vertical, as measured by an observer stationary on the ground. An observer on the train, however, sees the drops fall perfectly
A 200-m-wide river flows due east at a uniform speed of 2.0 m/s. A boat with a speed of 8.0 m/s relative to the water leaves the south bank pointed in a direction 30o west of north. What are the(a) Magnitude and(b) Direction of the boat's velocity relative to the ground?(c) How long does the boat
Two highways intersect as shown in Figure. At the instant shown, a police car P is distance d p = 800 m from the intersection and moving at speed vp = 80 km/h. Motorist M is distance dM = 600 m from the intersection and moving at speed vM = 60 km/h. (a) In unit-vector notation, what is the velocity
In the overhead view of Figure, Jeeps P and B race along straight lines, across flat terrain, and past stationary border guard A. Relative to the guard, B travels at a constant speed of 20.0 m/s, at the angle θ2 = 30.0o. Relative to the guard, P has accelerated from rest at a constant rate of
Ship A is located 4.0 km north and 2.5 km east of ship B. Ship A has a velocity of 22km/h toward the south, and ship B has a velocity of 40km/h in a direction 37o north of east.(a) What is the velocity of A relative to B in unit-vector notation with i toward the east?(b) Write an expression (in
A 200-m-wide river has a uniform flow speed of 1.1 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 4.0 m/s with respect to the water. There is a clearing on the north bank
You are kidnapped by political-science majors (who are upset because you told them political science is not a real science). Although blindfolded, you can tell the speed of their car (by the whine of the engine), the time of travel (by men tally counting off seconds), and the direction of travel
Curtain of death, a large metallic asteroid strikes Earth and quickly digs a crater into the rocky material below ground level by launching rocks upward and outward. The following table gives five pairs of launch speeds and angles (from the horizontal) for such rocks, based on a model of crater
In Figure, a lump of wet putty moves in uniform circular motion as it rides at a radius of 20.0 cm on the rim of a wheel rotating counterclockwise with a period of 5.00ms. The lump then happens to fly off the rim at the 5 o'clock position (as if on a clock face). It leaves the rim at a height of h
A particle is in uniform circular motion about the origin of a xy coordinate system, moving clockwise with a period of 7.00 s. At one instant, its position vector (from the origin) is r = (2.00 m) i - (3.00m) j. At that instant, what is its velocity in unit-vector notation?
In Figure, a ball is shot directly upward from the ground with an initial speed of v0 =7.00 m/s, simultaneously a construction elevator cab begins to move upward from the ground with a constant speed of v c = 3.00 m/s. What maximum height does the ball reach relative to? (a) The ground and (b) The
In Figure a, a sled moves in the negative x direction at constant speed u, while a ball of ice is shot from the sled with a velocity v0 = v0xi + v0yj relative to the sled. When the ball lands, its horizontal displacement ??xbg relative to the ground (from its launch position to its landing
A woman who can row a boat at 6.4 km/h in still water faces a long, straight river with a width of 6.4 km and a current of 3 .2km/h. Let i point directly across the river and j point directly downstream. If she rows in a straight line to a point directly opposite her starting position,(a) At what
In Figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d1 = 360 m from the station and at angle θ1 = 40o above the horizon. The airplane is tracked through an angular change ??θ = 123o in the vertical east-west plane;
A rifle is aimed horizontally at a target 30 m away. The bullet hits the target 1.9 cm below the aiming point. What are?(a) The bullet's time of flight and(b) Its speed as it emerges from the rifle?
The fast French train known as the TGV (Train b Grande Vitesse) has a scheduled average speed of 216 km/h.(a) If the train goes around a curve at that speed and the magnitude of the acceleration experienced by the passengers is to be limited to 0.050g what is the smallest radius of curvature for
A magnetic field can force a charged particle to move in a circular path. Suppose that an electron moving in a circle experiences a radial acceleration of magnitude 3.0 x 1014m/s2 in a particular magnetic field.(a) What is the speed of the electron if the radius of its circular path is 15 cm?(b)
The position vector for a proton is initially r = 5.0i – 6.0j + 2.0k and then later is r = – 2.0i + 6.0i + 2.0k, all in meters.(a) What is the proton's displacement vector, and(b) To what plane is that vector parallel?
A particle P travels with constant speed on a circle of radius r = 3.00m (Figure) and completes one revolution in 20.0 s. The particle passes through O at time t = 0. State the following vectors in magnitude-angle notation (angle relative to the positive direction of x). With respect to O, find the
An iceboat sails across the surface of a frozen lake with constant acceleration produced by the wind. At a certain instant the boat's velocity is (6.30i – 8.42j) m/s. Three seconds later, because of a wind shift, the boat is instantaneously at rest. What is its average acceleration for this 3 s
In 3.50 h, o balloon drifts 21.5 km north, 9.70 km east, and 2.88 km upward from its release point on the ground. Find(a) The magnitude of its average velocity and(b) The angle its average velocity makes with the horizontal.
A ball is thrown horizontally from a height of 20m and hits the ground with a speed that is three times its initial speed. What is the initial speed?
A projectile is launched with an initial speed of 30 m/s at an angle of 60o above the horizontal. What are the(a) Magnitude and(b) Angle of its velocity 2.0 s after launch, and(c) Is the angle above or below the horizontal? What are the(d) Magnitude and(e) Angle of its velocity 5.0 s after launch,
An airport terminal has a moving sidewalk to speed passengers through a long corridor. Larry does not use the moving sidewalk; he takes 150 s to walk through the corridor. Curly, who simply stands on the moving sidewalk, covers the same distance in 70 s. Moe boards the sidewalk and walks along it.
A football player punts the football so that it will have a "hang time" (time of flight) of 4.5 s and land 46 m away. If the ball leaves the player's foot 150 cm above the ground, what must be the(a) Magnitude and(b) Angle (relative to the horizontal) of the ball's initial velocity?
For women's volleyball the top of the net is 2.24 m above the floor and the court measures 9.0 m by 9.0 m on each side of the net. Using a jump serve, a player strikes the ball at a point that is 3.0 m above the floor and a horizontal distance of 8.0 m from the net. If the initial velocity of the
Figure shows the straight path of a particle across an xy coordinate system as the particle is accelerated from rest during time interval ∆t1. The acceleration is constant. The xy coordinates for point A are (4.00 m, 6.00 m); those for point B are (12.0 m, 18.0 m).(a) What is the ratio ay/ax of
An astronaut is rotated in a horizontal centrifuge at a radius of 5.0 m.(a) What is the astronaut's speed if the centripetal acceleration has a magnitude of 7.09?(b) How many revolutions per minute are required to produce this acceleration?(c) What is the period of the motion?
(a) What is the magnitude of the centripetal acceleration of an object on Earth's equator due to the rotation of Earth?(b) What would Earth's rotation period have to be for objects on the equator to have a centripetal acceleration of magnitude 9.8 m/s2?
A person walks up a stalled l5-m-long escalator in 90s. When standing on the same escalator, now moving, the person is carried up in 60s. How much time would it take that person to walk up the moving escalator? Does the answer depend on the length of the escalator?
A baseball is hit at ground level. The ball reaches its maximum height above ground level 3.0 s after being hit. Then 2.5 s after reaching its maximum height, the ball barely clears a fence that is 97.5 m from where it was hit. Assume the ground is level.(a) What maximum height above ground level
The range of a projectile depends not only on v0 and θ0 but also on the value g of the free-fall acceleration, which varies from place to place. In 1936, Jesse Owens established a world's running broad jump record of 8.09 m at the Olympic Games at Berlin (where g = 9.8128 m/s2). Assuming the same
During volcanic eruptions, chunks of solid rock can be blasted out of the volcano; these projectiles are called volcanic bombs. Figure shows a cross section of Mt. Fuji, in Japan. (a) At what initial speed would a bomb have to be ejected, at angle θ0 = 35o to the horizontal from the vent at A in
Long flights at mid latitudes in the Northern Hemisphere encounter the jet stream, &r eastward airflow that can affect a plane's speed relative to Earth's surface, if a pilot maintains a certain speed relative to the air (the plane's airspeed), the speed relative to the surface (the plane's
A particle starts from the origin at t = 0 with a velocity of 8.0j m/s and moves in the xy plane with constant acceleration (4.0i + 2.0j) m/s2. When the particle's x coordinate is 29 m, what are its(a) y coordinate and(b) Speed?
A sprinter running on a circular track has a velocity of constant magnitude 9.2m/s and a centripetal acceleration of magnitude 3.8 m/s2. What are?(a) The track radius and(b) The period of the circular motion?
An electron having an initial horizontal velocity of magnitude 1.00 x 109 cm/s travels into the region between two horizontal metal plates that are electrically charged. In that region, the electron travels a horizontal distance of 2.00 cm and has a constant downward acceleration of magnitude 1.00
An elevator without a ceiling is ascending with a constant speed of 10 m/s. A boy on the elevator shoots a ball directly upward, from a height of 2.0 m above the elevator floor, just as the elevator floor is 28 m above the ground. The initial speed of the ball with respect to the elevator is 20
Suppose that a space probe can withstand the stresses of a 20 g acceleration.(a) What is the minimum turning radius of such a craft moving at a speed of one-tenth the speed of light?(b) How long would it take to complete a 90o turn at this speed?
At what initial speed must the basketball player in Figure throw the ball, at angle θ0 = 55o above the horizontal, to make the foul shot? The horizontal distances are θ0 = 1.0 ft and d2 = 14 ft, and the heights are h1 = 7.0 ft and h2 = 10ft.
A wooden boxcar is moving along a straight railroad track at speed v1. A sniper fires a bullet (initial speed v2) at it from a high-powered rifle. The bullet passes through both lengthwise walls of the car, its entrance and exit holes being exactly opposite each other as viewed from within the car.
You are to throw a ball with a speed of 12.0 m/s at a target that is height h = 5.00 m above the level at which you release the ball (Figure).You want the ball's velocity to be horizontal at the instant it reaches the target. (a) At what angle θ above the horizontal must you throw the ball? (b)
Figure shows the path taken by a drunk skunk over level ground, from initial point i to final point f. The angles are θ1 = 30.0o, θ2 = 50.0o, and θ3 = 80.0o, and the distances are d1 = 5.00 d2 = 8.00m, and d3 =12.0 m. What are the (a) Magnitude and (b) Angle of the skunk's displacement from i to

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