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physics
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Physics 5th edition James S. Walker - Solutions

Wrongly called for a foul, an angry basketball player throws the ball straight down to the floor. If the ball bounces straight up and returns to the floor 3.2 s after first striking it, what was the ball's greatest height above the floor?
You drive your car in a straight line at 15 m/s for 10 minutes, then at 25 m/s for another 10 minutes.(a) Is your average speed for the entire trip greater than, less than, or equal to 20 m/s?(b) Choose the best explanation from among the following:I. More time is required to drive at 15 m/s than
To celebrate a victory, a pitcher throws her glove straight upward with an initial speed of 6.5 m/s. (a) How much time does it take for the glove to return to the pitcher? (b) How much time does it take for the glove to reach its maximum height?
Standing at the edge of a cliff 30.5 m high, you drop a ball. Later, you throw a second ball downward with an initial speed of 11.2 m/s.(a) Which ball has the greater increase in speed when it reaches the base of the cliff, or do both balls speed up by the same amount?(b) Verify your answer to part
You shoot an arrow into the air. Two seconds later (2.00 s) the arrow has gone straight upward to a height of 30.0 m above its launch point.(a) What was the arrow's initial speed?(b) How much time did it take for the arrow to first reach a height of 15.0 m above its launch point?
While riding on an elevator descending with a constant speed of 3.0 m / s, you accidentally drop a book from under your arm.(a) How much time does it take for the book to reach the elevator floor, 1.2 m below your arm?(b) What is the book's speed relative to you when it hits the elevator floor?
A hot-air balloon is descending at a rate of 2.3 m/s when a passenger drops a camera. If the camera is 41 m above the ground when it is dropped,(a) How much time does it take for the camera to reach the ground,(b) What is its velocity just before it lands? Let upward be the positive direction for
A model rocket blasts off and moves upward with an acceleration of 12 m/s2 until it reaches a height of 29 m, at which point its engine shuts off and it continues its flight in free fall. (a) What is the maximum height attained by the rocket? (b) What is the speed of the rocket just before it hits
The southern flying squirrel (Glaucomys volans) can reduce its free-fall acceleration by extending a furry membrane called a patagium and gliding through the air. FIGURE 2-41 shows the vertical position-versus-time plot of one squirrel's flight. Use the information given in the plot to determine
A young woman at a carnival steps up to the "high striker," a popular test of strength where the contestant hits one end of a lever with a mallet, propelling a small metal plug upward toward a bell. She gives the mallet a mighty swing and sends the plug to the top of the striker, where it rings the
While sitting on a tree branch 10.0 m above the ground, you drop a chestnut. When the chestnut has fallen 2.5 m, you throw a second chestnut straight down. What initial speed must you give the second chestnut if they are both to reach the ground at the same time?
An astronaut on the Moon drops a rock straight downward from a height of 1.25 m. If the acceleration of gravity on the Moon is 1.62 m/s2, what is the speed of the rock just before it lands?
Usain Bolt of Jamaica set a world record in 2009 for the 200-meter dash with a time of 19.19 seconds. What was his average speed? Give your answer in meters per second and miles per hour.
An elevator in the Taipei 101 skyscraper can start from rest and accelerate to a maximum speed of 16 m/s with a constant acceleration of 1.1 m/s2. Through what distance does the elevator move as it accelerates to its maximum speed?
Geologists have learned of periods in the past when the Strait of Gibraltar closed off, and the Mediterranean Sea dried out and become a desert. Later, when the strait reopened, a massive saltwater waterfall was created. According to geologists, the water in this waterfall was supersonic; that is,
A juggler throws a ball straight up into the air. If the ball returns to its original position in the juggler's hand in 0.98 s, what was its maximum height above the juggler's hand?
At the edge of a roof you drop ball A from rest, and at the same instant your friend throws ball B upward from the ground with an initial velocity of v0 sufficient to reach your position on the roof. What are the signs (positive or negative) of the velocity and the acceleration of each ball at a
Two balls start their motion at the same time, with ball A dropped from rest and ball B thrown upward with an initial speed v0. Which of the five plots shown in FIGURE 2-43 corresponds to(a) Ball A(b) Ball B?In figure 2-43
Refer to the position-versus-time plot in FIGURE 2-44 for the following questions:In figure 2-44
NASA operates a 2.2-second drop tower at the Glenn Research Center in Cleveland, Ohio. At this facility, experimental packages are dropped from the top of the tower, on the 8th floor of the building. During their 2.2 seconds of free fall, the packages experience a microgravity environment similar
The velocity-versus-time graph for an object moving in a straight line is given in FIGURE 2-45.(a) What is the acceleration of this object?(b) If this object is at x = 12.0 m at time t = 0, what is its position at t = 1.00 s?(c) Assuming the acceleration of the object remains constant, what is its
At the 18th green of the U.S. Open you need to make a 23.5-ft putt to win the tournament. When you hit the ball, giving it an initial speed of 1.54 m/s, it stops 6.00 ft short of the hole.(a) Assuming the deceleration caused by the grass is constant, what should the initial speed have been to just
A glaucous-winged gull, ascending straight upward at 5.20 m/s, drops a shell when it is 12.5 m above the ground.(a) What are the magnitude and direction of the shell's acceleration just after it is released?(b) Find the maximum height above the ground reached by the shell.(c) How much time does it
Suppose that each component of a certain vector is doubled. (a) By what multiplicative factor does the magnitude of the vector change? (b) By what multiplicative factor does the direction angle of the vector change?
A vector has the components Ax = 22 m and Ay = 13 m.(a) What is the magnitude of this vector?(b) What angle does this vector make with the positive x axis?
A vector has the components Ax = - 36 m and Ay = 43 m.(a) What is the magnitude of this vector?(b) What angle does this vector make with the positive x axis?
A baseball "diamond" (FIGURE 3-38) is a square with sides 90 ft in length. If the positive x axis points from home plate to first base, and the positive y axis points from home plate to third base, find the displacement vector of a base runner who has just hit(a) A double,(b) A triple,(c) A home
A lighthouse that rises 49 ft above the surface of the water sits on a rocky cliff that extends 19 ft from its base, as shown in FIGURE 3-39. A sailor on the deck of a ship sights the top of the lighthouse at an angle of 30.0° above the horizontal. If the sailor's eye level is 14 ft above the
A water molecule is shown schematically in FIGURE 3-40. The distance from the center of the oxygen atom to the center of a hydrogen atom is 0.96 Ã…, and the angle between the hydrogen atoms is 104.5°. Find the center-to-center distance between the hydrogen atoms. (1 Ã… =
(a) The direction(b) The magnitude of the vector r >.(c) If both rx and ry are doubled, how do you predict your answers to parts (a) and (b) will change?(d) Verify your prediction in part (c) by calculating the magnitude and direction for this new case.
You drive a car 680 ft to the east, then 340 ft to the north.(a) What is the magnitude of your displacement?(b) Using a sketch, estimate the direction of your displacement.(c) Verify your estimate in part (b) with a numerical calculation of the direction.
(a) The greater x component,(b) The greater y component?
A treasure map directs you to start at a palm tree and walk due north for 15.0 m. You are then to turn 90° and walk 22.0 m; then turn 90° again and walk 5.00 m. Give the distance from the palm tree, and the direction relative to north, for each of the four possible locations of the treasure.
A whale comes to the surface to breathe and then dives at an angle of 20.0° below the horizontal (FIGURE 3-41). If the whale continues in a straight line for 215 m,(a) How deep is it, and(b) How far has it traveled horizontally?
Rank the vectors in FIGURE 3-37 in order of increasing magnitude.
Consider the vectors A and B(vector) shown in FIGURE 3-42. Which of the other four vectors in the figure C(vector), D(vector), E(vector), and F(vector)) best represents the direction of(a) A(vector) + B(vector),(b) A(vector) €“ B(vector),(c) B(vector) €“ A(vector)?
Refer to Figure 3-42 for the following questions:
A vector A has a magnitude of 40.0 m and points in a direction 20.0° below the positive x axis. A second vector, B, has a magnitude of 75.0 m and points in a direction 50.0° above the positive x axis.(a) Sketch the vectors A, B, and C = A + B.(b) Using the component method of vector addition,
An air traffic controller observes two airplanes approaching the airport. The displacement from the control tower to plane 1 is given by the vector A(vector), which has a magnitude of 220 km and points in a direction 32° north of west. The displacement from the control tower to plane 2 is given by
The initial velocity of a car, v(vector)i, is 45 km/h in the positive x direction. The final velocity of the car, v(vector)f, is 66 km/h in a direction that points 75° above the positive x axis.(a) Sketch the vectors – v(vector)i, v(vector)f, and Δv(vector) = v(vector)f – v(vector)i.(b) Find
Vector A points in the positive x direction and has a magnitude of 75 m. The vector C = A + B points in the positive y direction and has a magnitude of 95 m.(a) Sketch (vector)A, (vector)B, and (vector)C.(b) Estimate the magnitude and direction of the vector B.(c) Verify your estimate in part (b)
Vector A(vector) points in the negative x direction and has a magnitude of 22 units. The vector B(vector) points in the positive y direction.(a) Find the magnitude of B(vector) if A(vector) + B(vector) has a magnitude of 37 units.(b) Sketch A(vector) and B(vector).
Vector A points in the negative y direction and has a magnitude of 5 units. Vector B has twice the magnitude and points in the positive x direction. Find the direction and magnitude of(a) A(vector) + B(vector),(b) A(vector) – NB(vector),(c) B(vector) – A(vector).
(a) The graphical method and(b) The component method of vector addition. Compare your results.
A particle undergoes a displacement Δr(vector) of magnitude 54 m in a direction 42° below the x axis. Express Δr(vector) in terms of the unit vectors x̂ and ŷ.
Rank the vectors in Figure 3-37 in order of increasing value of their x component.
A vector has a magnitude of 3.50 m and points in a direction that is 145° counterclockwise from the x axis. Find the x and y components of this vector.
A vector A has a length of 6.1 m and points in the negative x direction. Find(a) The x component(b) The magnitude of the vector – 3.7 A.
The vector – 5.2 A has a magnitude of 34 m and points in the positive x direction. Find(a) The x component(b) The magnitude of the vector A.
Find the direction and magnitude of the vectors.
Find the direction and magnitude of the vectors.
For the vectors given in Problem 34, expressa. (vector)A - (vector)Bb. (vector)B - (vector)A unit vector notation.
Express each of the vectors in FIGURE 3-44 in unit vector notation.
Referring to the vectors in Figure 3-44, express the sum A(vector) + B(vector) + C(vector) in unit vector notation.
The blue curves shown in FIGURE 3-45 display the constant-speed motion of two different particles in the x-y plane. For each of the eight vectors in Figure 3-45, state whether it is(a) A position vector,(b) A velocity vector,(c) An acceleration vector for the particles.
What are the direction and magnitude of your total displacement if you have traveled due west with a speed of 23 m/s for 175 s, then due south at 12 m/s for 285 s?
Rank the vectors in Figure 3-37 in order of increasing value of their y component.
Two of the allowed chess moves for a knight are shown in FIGURE 3-46.(a) Is the magnitude of displacement 1 greater than, less than, or equal to the magnitude of displacement 2? Explain.(b) Find the magnitude and direction of the knight's displacement for each of the two moves. Assume that the
To visit your favorite ice cream shop, you must travel 490 m west on Main Street and then 950 m south on Division Street.(a) Find the total distance you traveled.(b) Write your displacement vector in unit vector notation, taking the x̂ direction to be east and the ŷ direction to be north.(c)
Referring to Problem 41, suppose you take 44 s to complete the 490-m displacement and 73 s to complete the 950-m displacement.In Problem 41To visit your favorite ice cream shop, you must travel 490 m west on Main Street and then 950 m south on Division Street.(a) What are the magnitude and
You drive a car 1500 ft to the east, then 2500 ft to the north. If the trip took 3.0 minutes, what were the direction and magnitude of your average velocity?
A jogger runs with a speed of 3.25 m/s in a direction 30.0° above the x axis.(a) Find the x and y components of the jogger's velocity.(b) How will the velocity components found in part (a) change if the jogger's speed is halved? (c) Calculate the components of the velocity for the case where
You throw a ball upward with an initial speed of 4.5 m/s. When it returns to your hand 0.92 s later, it has the same speed in the downward direction (assuming air resistance can be ignored). What was the average acceleration vector of the ball?
Consider a skateboarder who starts from rest at the top of a ramp that is inclined at an angle of 17.5° to the horizontal. Assuming that the skateboarder's acceleration is g sin 17.5°, find his speed when he reaches the bottom of the ramp in 3.25 s.
In a soccer game a midfielder kicks the ball from one touchline directly toward the other with a velocity of (14.0 m/s) x̂. After the ball travels for 2.50 s, a striker makes an acrobatic kick that gives the ball a new velocity in the ŷ direction, and after 0.900 s the ball passes the diving
The accompanying photo shows a KC-10A Extender using a boom to refuel an aircraft in flight. If the velocity of the KC-10A is 125 m/s due east relative to the ground, what is the velocity of the aircraft being refueled relative to(a) The ground,(b) The KC-10A?
As an airplane taxies on the runway with a speed of 16.5 m/s, a flight attendant walks toward the tail of the plane with a speed of 1.22 m/s. What is the flight attendant's speed relative to the ground?
The press box at a baseball park is 44.5 ft above the ground. A reporter in the press box looks at an angle of 13.4° below the horizontal to see second base. What is the horizontal distance from the press box to second base?
Referring to part (a) of Example 3-11, find the time it takes for the boat to reach the opposite shore if the river is 35 m wide.
A police car travels at 38.0 m/s due east while in pursuit of a vehicle that is traveling at 33.5 m/s due east.(a) What is the velocity of the vehicle relative to the police car?(b) What is the velocity of the police car relative to the vehicle?
Consider the river crossing problem in Example 3-11. Suppose we would like the boat to move directly across the river (in the positive x direction) with a speed of 5.0 m/s. What is the corresponding speed and direction of the boat's velocity relative to the water?
As you hurry to catch your flight at the local airport, you encounter a moving walkway that is 61 m long and has a speed of 2.2 m/s relative to the ground. If it takes you 49 s to cover 61 m when walking on the ground, how much time will it take you to cover the same distance on the walkway? Assume
In Problem 53, how much time would it take you to cover the 61-m length of the walkway if, once you get on the walkway, you immediately turn around and start walking in the opposite direction with a speed of 1.3 m/s relative to the walkway?In problem 53As you hurry to catch your flight at the local
The pilot of an airplane wishes to fly due north, but there is a 65-km/h wind blowing toward the east.(a) In what direction relative to north should the pilot head her plane if its speed relative to the air is 340 km/h?(b) Draw a vector diagram that illustrates your result in part (a).(c) If the
A passenger walks from one side of a ferry to the other as it approaches a dock. If the passenger's velocity is 1.50 m/s due north relative to the ferry, and 4.50 m/s at an angle of 30.0° west of north relative to the water, what are the direction and magnitude of the ferry's velocity relative to
You are riding on a Jet Ski at an angle of 35° upstream on a river flowing with a speed of 2.8 m/s. If your velocity relative to the ground is 9.5 m/s at an angle of 20.0° upstream, what is the speed of the Jet Ski relative to the water?
In Problem 57, suppose the Jet Ski is moving at a speed of 11 m/s relative to the water.(a) At what angle must you point the Jet Ski if your velocity relative to the ground is to be perpendicular to the shore of the river?(b) If you increase the speed of the Jet Ski relative to the water, does the
Two people take identical Jet Skis across a river, traveling at the same speed relative to the water. Jet Ski A heads directly across the river and is carried downstream by the current before reaching the opposite shore. Jet Ski B travels in a direction that is 35° upstream and arrives at the
You are driving up a long, inclined road. After 1.2 miles you notice that signs along the roadside indicate that your elevation has increased by 530 ft. (a) What is the angle of the road above the horizontal? (b) How far do you have to drive to gain an additional 150 ft of elevation?
Consider the vectors A(vector) = (1.2 m) x̂ and B(vector) = 1-3.4 m2xn .(a) Is the magnitude of vector A(vector) greater than, less than, or equal to the magnitude of vector B?(b) Choose the best explanation from among the following:I. The number 3.4 is greater than the number 1.2.II. The
Two vectors are defined as follows: A(vector)= (–3.8 m) x̂ and B(vector) = (2.1 m)ŷ.(a) Is the magnitude of A(vector) + B(vector) greater than, less than, or equal to the magnitude of A(vector) – B(vector) ?(b) Choose the best explanation from among the following:I. A vector sum
To be compliant with regulations the inclination angle of a wheelchair ramp must not exceed 4.76°. If the wheelchair ramp must have a vertical height of 1.22 m, what is its minimum horizontal length?
Find the direction and magnitude of the vector 2 A(vector) + B(vector), where A(vector) = (12.1 m) x̂ and B(vector) = (–32.2 m)ŷ.
The components of a vector A̅ satisfy Ax < 0 and Ay < 0. Is the direction angle of A̅ between 0° and 90°, between 90° and 180°, between 180° and 270°, or between 270° and 360°?
The components of a vector B̅ satisfy Bx > 0 and By < 0. Is the direction angle of B̅ between 0° and 90°, between 90° and 180°, between 180° and 270°, or between 270° and 360°?
It is given that A(vector) – B(vector) = (– 51.4 m) x̂, C(vector) = (62.2 m) x̂, and A(vector) + B(vector) + C(vector) = (13.8 m) x̂. Find the vectors A(vector) and B(vector).
You pilot an airplane with the intent to fly 392 km in a direction 55.0° south of east from the starting airport. Air traffic control requires you to first fly due south for 85.0 km.(a) After completing the 85.0-km flight due south, how far are you from your destination?(b) In what direction
Find the x, y, and z components of the vector A(vector) shown in FIGURE 3-47, given that A = 65 m.
Observer 1 rides in a car and drops a ball from rest straight downward, relative to the interior of the car. The car moves horizontally with a constant speed of 3.50 m/s relative to observer 2 standing on the sidewalk.(a) What is the speed of the ball 1.00 s after it is released, as measured by
A road that rises 1 ft for every 100 ft traveled horizontally is said to have a 1% grade. Portions of the Lewiston grade, near Lewiston, Idaho, have a 6% grade. At what angle is this road inclined above the horizontal?
A person riding in a subway train drops a ball from rest straight downward, relative to the interior of the train. The train is moving horizontally with a constant speed of 6.7 m/s. A second person standing at rest on the subway platform observes the ball drop. From the point of view of the person
A football is thrown horizontally with an initial velocity of (16.6 m/s) x̂. Ignoring air resistance, the average acceleration of the football over any period of time is (- 9.81 m/s)2 ŷ.(a) Find the velocity vector of the ball 1.75 s after it is thrown.(b) Find the magnitude and direction of the
As a function of time, the velocity of the football described in Problem 71 can be written as v(vector) = (16.6 m/s)x̂ – [(9.81 m/s2)t]ŷ. Calculate the average acceleration vector of the football for the time periods(a) t = 0 to t = 1.00 s,(b) t = 0 to t = 2.50 s,(c) t = 0 to t = 5.00 s.
Two airplanes taxi as they approach the terminal. Plane 1 taxies with a speed of 12 m/s due north. Plane 2 taxies with a speed of 7.5 m/s in a direction 20° north of west.(a) What are the direction and magnitude of the velocity of plane 1 relative to plane 2?(b) What are the direction and
A shopper at the supermarket follows the path indicated by vectors A(vector), B(vector), C(vector), and D(vector) in FIGURE 3-48. Given that the vectors have the magnitudes A = 51 ft, B = 45 ft, C = 35 ft, and D = 13 ft, find the total displacement of the shopper using(a) The graphical method(b)
A food particle from your breakfast takes a circuitous path through your digestive system. Suppose its motion over a period of time can be represented by the four displacement vectors depicted in FIGURE 3-49. Let the vectors have magnitudes A = 8.0 cm, B = 16 cm, C = 23 cm, and D = 5.6 cm.(a) What
Initially, a particle is moving at 4.10 m/s at an angle of 33.5° above the horizontal. Two seconds later, its velocity is 6.05 m/s at an angle of 59.0° below the horizontal. What was the particle's average acceleration during these 2.00 seconds?
A passenger on a stopped bus notices that rain is falling vertically just outside the window. When the bus moves with constant velocity, the passenger observes that the falling raindrops are now making an angle of 15° with respect to the vertical.(a) What is the ratio of the speed of the raindrops
Suppose we orient the x axis of a two-dimensional coordinate system along the beach at Waikiki, as shown in FIGURE 3-50. Waves approaching the beach have a velocity relative to the shore given by v(vector)ws = (–1.3 m/s)ŷ. Surfers move more rapidly than the waves, but at an angle u to the
In 1759, John Harrison (1693-1776) completed his fourth precision chronometer, the H4, which eventually won the celebrated Longitude Prize. (For the human drama behind the Longitude Prize, see Longitude, by Dava Sobel.) When the minute hand of the H4 indicates 10 minutes past the hour, it extends

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