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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

Three of the fundamental constants of physics are the speed of light, c = 3.0 × 108 m/s, the universal gravitational constant, G = 6.7 × 10−11 m3 ⋅kg−1 ⋅s−2, and Planck's constant, h = 6.6 × 10−34 kg⋅ m2 ⋅ s −1. (a) Find a combination of these three constants that has the
Use dimensional analysis to determine how the period T of a swinging pendulum (the elapsed time for a complete cycle of motion) depends on some, or all, of these properties: the length L of the pendulum, the mass m of the pendulum bob, and the gravitational field strength g (in m/s2). Assume that
The Space Shuttle astronauts use a massing chair to measure their mass. The chair is attached to a spring and is free to oscillate back and forth. The frequency of the oscillation is measured and that is used to calculate the total mass m attached to the spring. If the spring constant of the spring
The average depth of the oceans is about 4 km, and oceans cover about 70% of Earth's surface. Make an order-of-magnitude estimate of the volume of water in the oceans. Do not look up any data in books. (Use your ingenuity to estimate the radius or circumference of Earth.)
The population of a culture of yeast cells is studied in the laboratory to see the effects of limited resources (food, space) on population growth. At 2-h intervals, the size of the population (measured as total mass of yeast cells) is recorded. (a) Make a graph of the yeast population as a
According to Kepler's third law, the orbital period T of a planet is related to the radius R of its orbit by T2 ∝ R3. Jupiter's orbit is larger than Earth's by a factor of 5.19. What is Jupiter's orbital period? (Earth's orbital period is 1 yr.)
Explain the difference between distance traveled, displacement, and displacement magnitude.
Explain the difference between speed and velocity.
On a graph of vx versus time, what quantity does the slope of the graph represent?
On a graph of x versus time, what quantity does the slope of the graph represent?
What is the relationship between average velocity and instantaneous velocity? An object can have different instantaneous velocities at different times. Can the same object have different average velocities? Explain.
Can the velocity of an object be zero and the acceleration be nonzero at the same time? Explain.
You are bicycling along a straight north-south road. Let the x -axis point north. Describe your motion in each of the following cases. Example: ax > 0 and vx > 0 means you are moving north and speeding up. (a) ax > 0 and vx < 0. (b) ax = 0 and vx < 0. (c) ax < 0 and vx = 0. (d) ax < 0 and vx <
A displacement of magnitude 32 cm toward the east is followed by displacements of magnitude 48 cm to the east and then 64 cm to the west. What is the total displacement?
Two cars, a Toyotayaris and a Jeep, are traveling in the same direction, although the Yaris is 186 m behind the Jeep. The speed of the Yaris is24.4 m/s and the speed of the Jeep is 18.6 m/s. How much time does it take for the Yaris to catch the Jeep?
Speedometer readings are obtained and graphed as a car comes to a stop along a straight-line path. How far does the car move between t = 0 and t = 16 s?
A graph is plotted of the vertical velocity vy of an elevator versus time. The y-axis points up.(a) How high is the elevator above the starting point (t = 0) after 20 s has elapsed?(b) When is the elevator at its highest location above the starting point?
A bicycle is moving along a straight line. The graph in the figure shows its position from the starting point as a function of time.(a) In which section(s) of the graph does the object have the highest speed?(b) At which time(s) does the object reverse its direction of motion?(c) How far does the
A ball thrown by a pitcher on a women's softball team is timed at 65.0 mph. The distance from the pitching rubber to home plate is 43.0 ft. In major league baseball the corresponding distance is 60.5 ft. If the batter in the softball game and the batter in the baseball game are to have equal times
A motor scooter travels east at a speed of 12 m/s. The driver then reverses direction and heads west at 15 m/s. What is the change in velocity of the scooter? Give magnitude and direction.
To pass a physical fitness test, Massimo must run 1000 m at an average rate of 4.0 m/s. He runs the first 900 m in 250 s. Is it possible for Massimo to pass the test? If so, how fast must he run the last 100 m to pass the test? Explain.
The graph shows speedometer readings, in meters per second (on the vertical axis), obtained as a skateboard travels along a straight-line path. How far does the board move between t = 3.00 s and t = 8.00 s?
The graph shows values of x (t) in meters, on the vertical axis, for a skater traveling in a straight line.(a) What is vav, x for the interval from t = 0 to t = 4.0 s?(b) From t = 0 to t = 5.0 s?
The graph shows values of x(t) in meters for a skater traveling in a straight line. What is vx at t = 2.0 s?
A squirrel is trying to locate some nuts he buried for the winter. He moves 4.0 m to the right of a stone and digs unsuccessfully. Then he moves 1.0 m to the left of his hole, changes his mind, and moves 6.5 m to the right of that position and digs a second hole. No luck. Then he moves 8.3 m to the
The graph shows values of x(t) in meters for an object traveling in a straight line. Plot vx as a function of time for this object from t = 0 to t = 8 s.
A chipmunk, trying to cross a road, first moves 80 cm to the right, then 30 cm to the left, then 90 cm to the right, and finally 310 cm to the left. (a) What is the chipmunk's total displacement? (b) If the elapsed time was 18 s, what was the chipmunk's average speed? (c) What was its average
Rita Jeptoo of Kenya was the first female finisher in the 110th Boston Marathon. She ran the first 10.0 km in a time of 0.5689 h. Assume the race course to be along a straight line. (a) What was her average speed during the first 10.0 km segment of the race? (b) She completed the entire race, a
A relay race is run along a straight-line track of length 300.0 m running south to north. The first runner starts at the south end of the track and passes the baton to a teammate at the north end of the track. The second runner races back to the start line and passes the baton to a third runner who
If a car traveling at 28 m/s is brought to a full stop in 4.0 s after the brakes are applied, find the average acceleration during braking.
An 1100-kg airplane starts from rest; 8.0 s later it reaches its takeoff speed of 35 m/s. What is the average acceleration of the airplane during this time?
A rubber ball is attached to a paddle by a rubber band. The ball is initially moving away from the paddle with a speed of 4.0 m/s. After 0.25 s, the ball is moving toward the paddle with a speed of 3.0 m/s. What is the average acceleration of the ball during that 0.25 s? Give magnitude and
(a) In Fig. 2.11, what is the instantaneous acceleration of the sports car of Example 2.5 at the time of 14 s from the start?In figure 2.11(b) What is the displacement of the car from t = 12.0 s to t = 16.0 s? (c) What is the average velocity of the car in the 4.0-s time interval from 12.0 s to
The graph with Problem 11 shows speedometer readings as a car comes to a stop. What is the magnitude of the acceleration at t = 7.0 s?In problem 11
A runner, jogging along a straight line path, starts at a position 60 m east of a milestone marker and heads west. After a short time interval he is20 m west of the mile marker. Choose east to be the positive x -direction. (a) What is the runner's displacement from his starting point? (b) What is
The figure shows a plot of vx(t) for a car traveling in a straight line.(a) What is a av, x between t = 6 s and t = 11 s?(b) What is vav, x for the same time interval?(c) What is vav, x for the interval t = 0 to t = 20 s?(d) What is the increase in the car's speed between 10 s and 15 s?(e) How far
The graph shows vx versus t for a body moving along a straight line.(a) What is ax at t = 11 s?(b) What is ax at t = 3 s?(c) How far does the body travel from t = 12 s to t = 14 s?
A toboggan is sliding in a straight line down a snowy slope. The table shows the speed of the toboggan at various times during its trip. (a) Make a graph of the speed as a function of time. (b) Judging by the graph, is it plausible that the toboggan's acceleration is constant? If so, what is the
The St. Charles streetcar in New Orleans starts from rest and has a constant acceleration of 1.20 m/s2 for 12.0 s. (a) Draw a graph of vx versus t. (b) How far has the train traveled at the end of the 12.0 s? (c) What is the speed of the train at the end of the 12.0 s? (d) Draw a motion
An airplane lands and starts down the runway with a southwest velocity of 55 m/s. What constant acceleration allows it to come to a stop in 1.0 km?
A train is traveling south at 24.0 m/s when the brakes are applied. It slows down with a constant acceleration to a speed of 6.00 m/s in a time of 9.00 s. (a) Draw a graph of vx versus t for a 12-s interval (starting 2 s before the brakes are applied and ending 1 s after the brakes are released).
A 1200-kg airplane starts from rest and moves forward with a constant acceleration of magnitude 5.00 m/s2 along a runway that is250 m long. (a) How long does it take the plane to reach a speed of 46.0 m/s? (b) How far along the runway has the plane moved when it reaches 46.0 m/s?
A car is speeding up and has an instantaneous velocity of 1.0 m/s in the + x -direction when a stopwatch reads 10.0 s. It has a constant acceleration of 2.0 m/s2 in the + x -direction. (a) What change in speed occurs between t = 10.0 s and t = 12.0 s? (b) What is the speed when the stopwatch
You are driving your car along a country road at a speed of 27.0 m/s. As you come over the crest of a hill, you notice a farm tractor 25.0 m ahead of you on the road, moving in the same direction as you at a speed of 10.0 m/s. You immediately slam on your brakes and slow down with a constant
A train is traveling along a straight, level track at 26.8 m/s (60.0 mi/h). Suddenly the engineer sees a truck stalled on the tracks 184 m ahead. If the maximum possible braking acceleration has magnitude 1.52 m/s2, can the train be stopped in time?
Johannes bicycles from his dorm to the pizza shop that is 3.00 mi east. Darren's apartment is located 1.50 mi west of Johannes's dorm. If Darren is able to meet Johannes at the pizza shop by bicycling in a straight line, what is the distance and direction he must travel?
In a cathode ray tube in an old TV, electrons are accelerated from rest with a constant acceleration of magnitude 7.03 × 1013 m/s2 during the first 2.0 cm of the tube's length; then they move at essentially constant velocity another 45 cm before hitting the screen. (a) Find the speed of the
The graph is of vx versus t for an object moving along the x -axis. How far does the object move between t = 9.0 s and t = 13.0 s? Solve using two methods: a graphical analysis and an algebraic solution.
The graph is of vx versus t for an object moving along the x -axis. What is the average acceleration between t = 5.0 s and t = 9.0 s? Solve using two methods: a graphical analysis and an algebraic solution.
A train, traveling at a constant speed of 22 m/s, comes to an incline with a constant slope. While going up the incline, the train slows down with a constant acceleration of magnitude 1.4 m/s2. (a) Draw a graph of vx versus t where the x -axis points up the incline. (b) What is the speed of the
A brick is thrown vertically upward with an initial speed of 3.00 m/s from the roof of a building. If the building is 78.4 m tall, how much time passes before the brick lands on the ground?
A penny is dropped from the observation deck of the Empire State building (369 m above ground). With what velocity does it strike the ground? The free-fall acceleration g = 9.80 m/s2 unless a more precise value is given in the problem statement. Ignore air resistance.
(a) How long does it take for a golf ball to fall from rest for a distance of 12.0 m? (b) How far would the ball fall in twice that time? The free-fall acceleration g = 9.80 m/s2 unless a more precise value is given in the problem statement. Ignore air resistance.
Grant Hill jumps 1.3 m straight up into the air to slam-dunk a basketball into the net. With what speed did he leave the floor?
During a walk on the Moon, an astronaut accidentally drops his camera over a 20.0-m cliff. It leaves his hands with zero speed, and after 2.0 s it has attained a velocity of 3.3 m/s downward. How far has the camera fallen after 4.0 s?
Glenda drops a coin from ear level down a wishing well. The coin falls a distance of 7.00 m before it strikes the water. If the speed of sound is 343 m/s, how long after Glenda releases the coin will she hear a splash?
At 3 p.m. a car is located 20 km south of its starting point. One hour later it is 96 km farther south. After two more hours, it is 12 km south of the original starting point. (a) What is the displacement of the car between 3 p.m. and 6 p.m.? (b) What is the displacement of the car from the
A stone is launched straight up by a slingshot. Its initial speed is 19.6 m/s and the stone is 1.50 m above the ground when launched. (a) How high above the ground does the stone rise? (b) How much time elapses before the stone hits the ground?
A 55-kg lead ball is dropped from the leaning tower of Pisa. The tower is 55 m high. (a) How far does the ball fall in the first 3.0 s of flight? (b) What is the speed of the ball after it has traveled 2.5 m downward? (c) What is the speed of the ball 3.0 s after it is released? (d) If the ball
A balloonist, riding in the basket of a hot air balloon that is rising vertically with a constant velocity of 10.0 m/s, releases a sandbag when the balloon is 40.8 m above the ground. What is the bag's speed when it hits the ground?
Superman is standing 120 m horizontally away from Lois Lane. A villain throws a rock vertically downward with a speed of 2.8 m/s from 14.0 m directly above Lois. (a) If Superman is to intervene and catch the rock just before it hits Lois, what should be his minimum constant acceleration? (b) How
A student, looking toward his fourth-floor dormitory window, sees a flowerpot with nasturtiums (originally on a window sill above) pass his2.0-m high window in 0.093 s. The distance between floors in the dormitory is 4.0 m. From a window on which floor did the flowerpot fall?
You drop a stone into a deep well and hear it hit the bottom 3.20 s later. This is the time it takes for the stone to fall to the bottom of the well, plus the time it takes for the sound of the stone hitting the bottom to reach you. Sound travels about 343 m/s in air. How deep is the well?
(a) If a freestyle swimmer traveled 1500 m in a time of 14 min 53 s, how fast was his average speed? (b) If the pool was rectangular and 50 m in length, how does the speed you found compare with his sustained swimming speed of 1.54 m/s during one length of the pool after he had been swimming for
While passing a slower car on the highway, you accelerate uniformly from 17.4 m/s to 27.3 m/s in a time of 10.0 s. (a) How far do you travel during this time? (b) What is your acceleration magnitude?
A cheetah can accelerate from rest to 24 m/s in 2.0 s. Assuming the acceleration is constant over the time interval, (a) What is the magnitude of the acceleration of the cheetah? (b) What is the distance traveled by the cheetah in these 2.0 s? (c) A runner can accelerate from rest to 6.0 m/s in
A rocket is launched from rest. After 8.0 min, it is 160 km above the Earth's surface and is moving at a speed of 7.6 km/s. Assuming the rocket moves up in a straight line, what are its (a) Average velocity (b) Average acceleration?
For the train of Example 2.2, find the average velocity between 3:14 p.m. when the train is at 3 km east of the origin and 3:28 p.m. when it is 10 km east of the origin.
A streetcar named Desire travels between two stations 0.60 km apart. Leaving the first station, it accelerates for 10.0 s at 1.0 m/s2 and then travels at a constant speed until it is near the second station, when it brakes at 2.0 m/s2 in order to stop at the station. How long did this trip take?
An unmarked police car starts from rest just as a speeding car passes at a speed of v. If the police car speeds up with a constant acceleration of magnitude a, what is the speed of the police car when it catches up to the speeder, who does not realize she is being pursued and does not vary her
A stone is thrown vertically downward from the roof of a building. It passes a window 16.0 m below the roof with a speed of 25.0 m/s. It lands on the ground 3.00 s after it was thrown. What was (a) The initial velocity of the stone (b) How tall is the building?
A car traveling at 29 m/s (65 mi/h) runs into a bridge abutment after the driver falls asleep at the wheel. (a) If the driver is wearing a seat belt and comes to rest within a 1.0-m distance, what is his acceleration (assumed constant)? (b) A passenger who isn't wearing a seat belt is thrown into
To pass a physical fitness test, Marcella must run 1000 m at an average speed of 4.00 m/s. She runs the first 500 m at an average of 4.20 m/s. (a) How much time does she have to run the last 500 m? (b) What should be her average speed over the last 500 m in order to finish with an overall average
At 3:00 p.m., a bank robber is spotted driving north on I-15 at milepost 126. His speed is 112.0 mi/h. At 3:37 p.m., he is spotted at milepost 185 doing 105.0 mi/h. During this time interval, what are the bank robber's displacement, average velocity, and average acceleration? (Assume a straight
Based on the information given in Problem 59, is it possible that the rocket moves with constant acceleration? Explain. In Problem 59, A rocket is launched from rest. After 8.0 min, it is 160 km above the Earth's surface and is moving at a speed of 7.6 km/s. Assuming the rocket moves up in a
An elevator starts at rest on the ninth floor. At t = 0, a passenger pushes a button to go to another floor. The graph for this problem shows the acceleration ay of the elevator as a function of time. Let the y -axis point upward.(a) Has the passenger gone to a higher or lower floor?(b) Sketch a
The graph for this problem shows the vertical velocity vy of a bouncing ball as a function of time. The y -axis points up. Answer these questions based on the data in the graph.(a) At what time does the ball reach its maximum height?(b) For how long is the ball in contact with the floor?(c) What is
A rocket engine can accelerate a rocket launched from rest vertically up with an acceleration of 20.0 m/s2.However, after 50.0 s of flight the engine fails. (a) What is the rocket's altitude when the engine fails? (b) When does it reach its maximum height? (c) What is the maximum height reached?
A cyclist travels 10.0 km east in a time of 11 min 40 s. What is his average velocity in meters per second?
The graph shows the position x of a switch engine in a rail yard as a function of time t. At which of the labeled times t0 to t7 is(a) ax (b) ax = 0,(c) ax > 0,(d) vx = 0,(e) The speed decreasing?
An airtrack glider, 8.0 cm long, blocks light as it goes through a photocell gate. The glider is released from rest on a frictionless inclined track and the gate is positioned so that the glider has traveled 96 cm when it is in the middle of the gate. The timer gives a reading of 333 ms for the
Find the point of no return for an airport runway of 1.50 mi in length if a jet plane can accelerate at 10.0 ft/s2 and decelerate at 7.00 ft/s2. The point of no return occurs when the pilot can no longer abort the takeoff without running out of runway. What length of time is available from the
In the human nervous system, signals are transmitted along neurons as action potentials that travel at speeds of up to 100 m/s. (An action potential is a traveling influx of sodium ions through the membrane of a neuron.) The signal is passed from one neuron to another by the release of
In a game against the White Sox, baseball pitcher Nolan Ryan threw a pitch measured at 45.1 m/s. If it was 18.4 m from Nolan's position on the pitcher's mound to home plate, how long did it take the ball to get to the batter waiting at home plate? Treat the ball's velocity as constant and ignore
Jason drives due west with a speed of 35.0 mi/h for 30.0 min, then continues in the same direction with a speed of 60.0 mi/h for 2.00 h, then drives farther west at 25.0 mi/h for 10.0 min. What is Jason's average velocity for the entire trip?
Give an example of an object whose acceleration is (1) in the same direction as its velocity, (2) opposite its velocity, and (3) perpendicular to its velocity.
Tell whether or not each of the following objects has a constant velocity and explain your reasoning. (a) A car driving around a curve at constant speed on a flat road. (b) A car driving straight up a 6 ° incline at constant speed. (c) The Moon.
Explain how to add two displacement vectors of magnitudes 3 L and 4 L so that the vector sum has magnitude (a) L; (b) 7 L; (c) 5 L.
Compare the advantages and disadvantages of the two methods of vector addition (graphical and algebraic).
Why is the muzzle of a rifle not aimed directly at the center of the target? Why is this more important at longer ranges?
Does the monkey, coconut, and hunter demonstration still work if the hunter is in a higher tree and the arrow is pointed downward at the monkey and coconut? Explain.
(a) Is it possible for the sum of two vectors to be smaller in magnitude than the magnitude of either vector? (b) Is it possible for the magnitude of the sum of two vectors to be larger than the sum of the magnitudes of the two vectors?
What is the distinction between a vector and a scalar quantity? Give two examples of each.
Is it possible for two identical projectiles with identical initial speeds, but with two different angles of elevation, to land in the same spot? Explain. Ignore air resistance and sketch the trajectories.
You are standing on a balcony overlooking the beach. You throw a ball straight up into the air with speed vi and throw an identical ball straight down with speed vi. Ignoring air resistance, how do the speeds of the balls compare just before they hit the ground?
Can the average speed and the magnitude of the average velocity ever be equal? If so, under what circumstances?
Displacement vector A is directed to the west and has magnitude 2.56 km. A second displacement vector is also directed to the west and has magnitude 7.44 km. (a) What are the magnitude and direction of A + B? (b) What are the magnitude and direction of A − B? (c) What are the magnitude and
A scout troop is practicing its orienteering skills with map and compass. First they walk due east for 1.2 km. Next, they walk 45°west of north for 2.7 km. In what direction must they walk to go directly back to their starting point? How far will they have to walk? Use graph paper, ruler, and
A person climbs from a Paris metro station to the street level by walking up a stalled escalator in 94 s. It takes 66 s to ride the same distance when standing on the escalator when it is operating normally. How long would it take for him to climb from the station to the street by walking up the
Prove that the displacement for a trip is equal to the vector sum of the displacements for each leg of the trip.

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