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physics
modern physics

University Physics With Modern Physics 2nd edition Wolfgang Bauer, Gary Westfall - Solutions

If you want to use a catapult to throw rocks and the maximum range you need these projectiles to have is 0.67 km, what initial speed do the rocks have to have as they leave the catapult
What is the maximum height above ground that a projectile of mass 0.790 kg, launched from ground level, can achieve if you are able to give it an initial speed of 80.3 m/s?
During one of the games, you were asked to punt for your football team. You kicked the ball at an angle of 35.0° with a velocity of 25.0 m/s. If your punt goes straight down the field, determine the average speed at which the running back of the opposing team standing at 70.0 m from you must run
By trial and error, a frog learns that it can leap a maximum horizontal distance of 1.30 m. If, in the course of an hour, the frog spends 20.0% of the time resting and 80.0% of the time performing identical jumps of that maximum length, in a straight line, what is the distance traveled by the frog?
A circus juggler performs an act with balls that she tosses with her right hand and catches with her left hand, Each ball is launched at an angle of 75.0° and reaches a maximum height of 90.0 cm above the launching height. If it takes the juggler 0.200 s to catch a ball with her left hand, pass it
In an arcade game, a ball is launched from the corner of a smooth inclined plane. The inclined plane makes a 30.0° angle with the horizontal and has a width of w = 50.0 cm. The spring-loaded launcher makes an angle of 45.0° with the lower edge of the inclined plane. The goal is to get the ball
A copy-cat daredevil tries to reenact F.vel Knievel's 1974 attempt to jump the Snake River Canyon in a rocket-powered motorcycle. The canyon is L. = 400. m wide, with the opposite rims at the same height. The height of the launch ramp at one rim of the canyon is h = 8.00 m above the rim, and the
A golf ball is hit with an initial angle of 35.5° with respect to the horizontal and an initial velocity of 83.3 mph. It lands a distance of 86.8 m away from where it was hit. By how much did the effects of wind resistance, spin, and so forth reduce the range of the golf ball from the ideal value?
You are walking on a moving walkway in an airport. The length of the walkway is 59.1 m. If your velocity relative to the walkway is 2.35 m/s and the walkway moves with a velocity of 1.77 m/s, how long will it take you to reach the other end of the walkway?
The captain of a boat wants to travel directly across a river that flows due east with a speed of 1.00 m/s. He starts from the south bank of the river and heads toward the north bank. The boat has a speed of 6.10 m/s with respect to the water. In what direction (in degrees) should the captain steer
The captain of a boat wants to travel directly across a river that flows due east. I le starts from the south bank of the river and heads toward the north bank. The boat has a speed of 5.57 m/s with respect to the water. The captain steers the boat in the direction 315°. How fast is the water
The air-speed indicator of a plane that took off from Detroit reads 350. km/h and the compass indicates that it is heading due east to Boston. A steady wind is blowing due north at 40.0 km/h. Calculate the velocity of the plane with reference to the ground. If the pilot wishes to fly directly to
You want to cross a straight section of a river that has a uniform current of 5.33 m/s and is 127. m wide. Your motorboat has an engine that can generate a speed of 17.5 m/s for your boat. Assume that you reach top speed right away (that is, neglect the time it takes to accelerate the boat to top
During a long airport layover, a physicist father and his 8-year-old daughter try a game that involves a moving walkway. They have measured the walkway to be 42.5 m long. The father has a stopwatch and times his daughter. First, the daughter walks with a constant speed in the same direction as the
An airplane has an air speed of 126.2 m/s and is flying due north, but the wind blows from the northeast to the southwest at 55.5 m/s. What is the plane's actual ground speed? Additional Exercises
A cannon is fired from a hill 116.7 m high at an angle of 22.7° with respect to the horizontal. If the muzzle velocity is 36.1 m/s, what is the speed of a 4.35-kg cannonball when it hits the ground 116.7 m below?
A baseball is thrown with a velocity of 31.1 m/s at an angle of θ = 33.4° above horizontal. What is the horizontal component of the ball's velocity at the highest point of the ball's trajectory?
A rock is thrown horizontally from the top of a building with an initial speed of v = 10.1 m/s. If it lands d = 57.1 m from the base of the building, how high is the building?
A car is moving at a constant 19.3 m/s, and rain is falling at 8.90 m/s straight down. What angle 0 (in degrees) does the rain make with respect to the horizontal as observed by the driver?
You tried to pass the salt and pepper shakers to your friend at the other end of a table of height 0.850 m by sliding them across the table. They both slid off the table, with velocities of 5.00 m/s and 2.50 m/s, respectively. a) Compare the times it takes the shakers to hit the floor. b) Compare
A box containing food supplies for a refugee camp was dropped from a helicopter flying horizontally at a constant elevation of 500. m. If the box hit the ground at a distance of 150. m horizontally from the point of its release, what was the speed of the helicopter? With what speed did the box hit
A car is driven straight off the edge of a cliff that is 60.0 m high. The police at the scene of the accident note that the point of impact is 150. m from the base of the cliff. How fast was the car traveling when it went over the cliff?
At the end of the spring term, a high school physics class celebrates by shooting a bundle of exam papers into the town landfill with a homemade catapult. They aim for a point that is 30.0 m away and at the same height from which the catapult releases the bundle. The initial horizontal velocity
Salmon often jump upstream through waterfalls to reach their breeding grounds. One salmon came across a waterfall 1.05 m in height, which she jumped in 2.10 s at an angle of 35.0° above the horizontal to continue upstream. What was the initial speed of her jump?
A firefighter, 60.0 m away from a burning building, directs a stream of water from a ground-level fire hose at an angle of 37.0° above the horizontal. If the water leaves the hose at 40.3 m/s, which floor of the building will the stream of water strike? Each floor is 4.00 m high.
A projectile leaves ground level at an angle of 68.0° above the horizontal. As it reaches its maximum height, H, it has traveled a horizontal distance, d, in the same amount of time. What is the ratio HUP.
The McNamara Delta terminal at the Metro Detroit Airport has moving walkways for the convenience of the passengers. Robert walks beside one walkway and takes 30.0 s to cover its length. John simply stands on the walkway and covers the same distance in 13.0 s. Kathy walks on the walkway with the
Rain is falling vertically at a constant speed of 7.00 m/s. At what angle from the vertical do the raindrops appear to be falling to the driver of a car traveling on a straight road with a speed of 60.0 km/h?
To determine the gravitational acceleration at the surface of a newly discovered planet, scientists perform a projectile motion experiment. They launch a small model rocket at an initial speed of 50.0 m/s and an angle of 30.0° above the horizontal and measure the (horizontal) range on flat ground
A diver jumps from a 40.0-m-high cliff into the sea. Rocks stick out of the water for a horizontal distance of 7.00 m from the foot of the cliff. With what minimum horizontal speed must the diver jump oil the cliff in order to clear the rocks and land safely in the sea?
An outfielder throws a baseball with an initial speed of 32.0 m/s .u an angle of 23.0° to the horizontal. The ball leaves his hand from a height of 1.83 m. How long is the ball in the air before it hits the ground?
A rock is tossed off the top of a cliff of height 34.9 m. Its initial speed is 29.3 m/s, and the launch angle is 29.9° above the horizontal. What is the speed with which the rock hits the ground at the bottom of the cliff?
During the 2004 Olympic Games, a shot putter threw a shot put with a speed of 13.0 m/s at an angle of 43.0° above the horizontal. She released the shot put from a height of 2.00 m above the ground.a) How far did the shot put travel in the horizontal direction?b) How long was it until the shot put
A salesman is standing on the Golden Gate Bridge in a traffic jam. He is at a height of 71.8 m above the water below. He receives a call on his cell phone that makes him so mad that he throws his phone horizontally off the bridge with a speed of 23.7 m/s.a) How far does the cell phone travel
A security guard is chasing a burglar across a rooftop, both running at 4.20 m/s. Before the burglar reaches the edge of the roof, he has to decide whether or not to try jumping to the roof of the next building, which is 5.50 m away and 4.00 m lower. If he decides to jump horizontally to get away
A blimp is ascending at the rate of 7.50 m/s at a height of 80.0 m above the ground when a package is thrown from its cockpit horizontally with a speed of 4.70 m/s.a) How long does it take for the package to reach the ground?b) With what velocity (magnitude and direction) does it hit the ground?
Wild geese are known for their lack of manners. One goose is flying northward at a level altitude of = 30.0 m above a north-south highway, when it sees a car ahead in the distance moving in the southbound lane and decides to deliver (drop) an "egg." The goose is flying at a speed of vg = 15.0
You are at the mall on the top step of a down escalator when you lean over laterally to see your 1.80-m-tall physics professor on the bottom step of the adjacent up escalator. Unfortunately, the ice cream you hold in your hand falls out of its cone as you lean. The two escalators have identical
A basketball player practices shooting three-pointers from a distance of 7.50 m from the hoop, releasing the ball at a height of 2.00 m above the floor. A standard basketball hoops rim top is 3.05 m above the floor. The player shoots the ball at an angle of 48.0° with the horizontal. At what
Wanting to invite Juliet to his party, Romeo is throwing pebbles at her window with a launch angle of 37.0° from the horizontal. He is launching the pebble 7.00 m below her window and 10.0 m from the base of the wall. What is the initial speed of the pebbles?
An airplane flies horizontally above the flat surface of a desert at an altitude of 5.00 km and a speed of 1000. km/h. If the airplane is to drop a bomb that is supposed to hit a target on the ground, where should the plane be with respect to the target when the bomb is released? If the target
A plane diving with constant speed, at an angle of 49.0° with the vertical, releases a package at an altitude of 600. m. The package hits the ground 3.50 s after release. How far horizontally does the package travel?
At a time of 10.0 s after being fired, a cannonball strikes a point 500. m horizontally from and 100. m vertically above the point of launch.a) With what initial velocity was the cannonball launched?b) What maximum height was attained by the ball?c) What is the magnitude and direction of the ball's
Neglect air resistance for the following. A soccer ball is kicked from the ground into the air. When the ball is at a height of 12.5 m, its velocity isa) To what maximum height will the ball rise?b) What horizontal distance will be traveled by the ball?c) With what velocity (magnitude and
For a Science Olympiad competition, a group of middle school students build a trebuchet that can fire a tennis ball from a height of 1.55 m with a velocity of 10.5 m/s and a launch angle of 35.0° above the horizontal. What horizontal distance will the tennis ball cover before it hits the ground?
A ceiling fan is rotating in clockwise direction (as viewed from below), but it is slowing down. What are the directions of w and α?
A hook above a stage is rated to support 150. lb. A 3.00-lb rope is attached to the hook, and a 147-lb actor is going to attempt to swing across the stage on the rope. Will the hook hold the actor up during the swing?
A popular carnival ride consists of seats attached to a central disk through cables, as shown in the figure. The passengers travel in uniform circular motion. The mass of one of the passengers (including the chair he is sitting on) is 65 kg; the mass of an empty chair on the opposite side of the
A person rides on a Ferris wheel of radius R, which is rotating at a constant angular velocity to. Compare the normal force of the seat pushing up on the person at point A to that at point B in the figure. Which force is greater, or are they the same?
Bicycle tires range in size from about 25.cm in diameter to about 70.cm in diameter. Why is it impractical to make tires much smaller than 25.cm in diameter?
A CD starts from rest and speeds up to the operating angular frequency of the CD player. Compare the angular velocity and acceleration of a point on the edge of the CD to those of a point halfway between the center and the edge of the CD. Do the same for the linear velocity and acceleration.
A car is traveling around an unbanked curve at a maximum speed. Which force(s) is (are) responsible for keeping it on the road?
Two masses hang from two strings of equal length that are attached to the ceiling of a car. One mass is over the driver's seat; the other is over the passenger's seat. As the car makes a sharp turn, both masses swing away from the center of the turn. In their resulting positions, will they be
A point mass m starts sliding from a height h along the frictionless surface shown in the figure. What is the minimum value of h in order for the mass to complete the loop of radius R?
In a conical pendulum, the bob attached to the string (which can be considered mass less) moves in a horizontal circle at constant speed. I he-string sweeps out a cone as the bob rotates. What forces are acting on the bob?
Is it possible to swing a mass attached to a string in a perfectly horizontal circle (with the mass and the string parallel to the ground)?
A small ice block of mass m starts from rest from the top of an inverted bowl in the shape of a hemisphere, as shown in the figure. The hemisphere is fixed to the ground, and the block slides without friction along the surface of the hemisphere. Find the normal force exerted by the block on the
Suppose you are riding on a roller coaster, which moves through a vertical circular loop. Show that your apparent weight at the bottom of the loop is six times your weight when you experience weightlessness at the top, independent of the size of the loop. Assume that friction is negligible.
The following event actually occurred on the Sunshine Skyway Bridge near St. Petersburg, Florida, in 1997. Five daredevils tied a 55-m-long cable to the center of the bridge. They hoped to swing back and forth under the bridge at the end of this cable. The five people (total weight = W) attached
What is the angle in radians that the Earth sweeps out in its orbit during winter?
Assuming that the Earth is spherical and recalling that latitudes range from 0° at the Equator to 90° N at the North Pole, how far apart, measured on the Earth's surface, are Dubuque, Iowa (42.50° N latitude), and Guatemala City (14.62° N latitude)? The two cities lie on approximately the same
Refer to the information given in Problem 9.32. If one could burrow through the Earth and dig a straight-line tunnel from Dubuque to Guatemala City, how long would the tunnel be? From the point of view of the digger, at what angle below the horizontal would the tunnel be directed?In problem
A baseball is thrown at approximately 88.0 mph and with a spin rate of 110. rpm. If the distance between the pitcher's point of release and the catcher's glove is 60.5 ft, how many full turns does the ball make between release and catch? Neglect any effect of gravity or air resistance on the ball's
A vinyl record plays at 33.3 rpm. Assume it takes 5.00 s for it to reach this lull speed, starting from rest.a) What is its angular acceleration during the 5.00 s?b) How many revolutions does the record make before reaching its final angular speed?
At a county fair, a boy takes his teddy bear on the giant Ferris wheel. Unfortunately, at the top of the ride, he accidentally drops his stuffed buddy. The wheel has a diameter of 12.0 m, the bottom of the wheel is 2.00 m above the ground and its rim is moving at a speed of 1.00 m/s. How far from
Having developed a taste for experimentation, the boy in Problem 9.36 invites two friends to bring their teddy bears on the same Ferris wheel. The boys are seated in positions 45.0° from each other. When the wheel brings the second boy to the maximum height, they all drop their stuffed animals. I
Mars orbits the Sun at a mean distance of 228 million km, in a period of 687 days. The Earth orbits at a mean distance of 149.6 million km, in a period of 365.26 days.a) Suppose Earth and Mars are positioned such that Earth lies on a straight line between Mars and the Sun. Exactly 365.26 days
Consider a large simple pendulum that is located at a latitude of 55.0o N and is swinging in a north-south direction with points A and B being the northernmost and the southernmost points of the swing, respectively. A stationary (with respect to the fixed stars) observer is looking directly down on
What is the centripetal acceleration of the Moon? The period of the Moon's orbit about the Earth is 27.3 days, measured with respect to the fixed stars. The radius of the Moon's orbit is RM = 3.85∙108 m.
You are holding the axle of a bicycle wheel with radius 35.0 cm and mass 1.00 kg. You get the wheel spinning at a rate of 75.0 rpm and then stop it by pressing the tire against the pavement. You notice that it takes 1.20 s for the wheel to come to a complete stop. What is the angular acceleration
Life scientists use ultracentrifuges to separate biological components or to remove molecules from suspension. Samples in a symmetric array of containers are spun rapidly about a central axis. The centrifugal acceleration they experience in their moving reference frame acts as "artificial gravity"
A centrifuge in a medical laboratory rotates at an angular speed of 3600. rpm (revolutions per minute). When switched off, it rotates 60.0 times before coming to rest. Find the constant angular acceleration of the centrifuge.
A discus thrower (with arm length of 1.20 m) starts from rest and gins to rotate counterclockwise with an angular acceleration of 2.50rad/s2.a) How long does it take the discus thrower's speed to get to 4.70rad/s?b) How many revolutions does the thrower make to reach the speed of 4.70rad/s?c) What
In a department store toy display, a small disk (disk 1) of radius 0.100 m is driven by a motor and j turns a larger disk (disk 2) of radius 0.500 m. Disk 2, in turn, drives disk 3, whose radius is 1.00 m. The three disks are in contact, and there is no slipping. Disk 3 is observed to sweep through
A particle is moving clockwise in a circle of radius 1.00 m. At a certain instant, the magnitude of its acceleration is a = |a| = 25.0 m/s2, and the acceleration vector has an angle of Î¸ = 50.0° with the position vector, as shown in the figure. At this instant, find the speed, v =
A small block of mass m is in contact with the inner wall of a large hollow cylinder. Assume the coefficient of static friction between the object and the wall of the cylinder is Î¼s. Initially, the cylinder is at rest, and the block is held in place by a peg supporting its weight. The cylinder
The motor of a fan turns a small wheel of radius rm = 2.00 cm. This wheel turns a belt, which is attached to a wheel of radius ri = 3.00 cm that is mounted to the axle of the fan blades. Measured from the center of this axle, the tip of the fan blades are at a distance rb = 15.0 cm. When the fan is
A car with a mass of 1000.kg goes over a hill at a constant speed of 60.0 m/s. The top of the hill can be approximated as an arc length of a circle with a radius of curvature of 370. m. What force does the car exert on the hill as it passes over the top?
Unlike a ship, an airplane does not use its rudder to turn. It turns by banking its wings: The lift force, perpendicular to the wings, has a horizontal component, which provides the centripetal acceleration for the turn, and a vertical component, which supports the plane's weight. (The rudder
An 80.0-kg pilot in an aircraft moving at a constant speed of 500.m/s pulls out of a vertical dive along an arc of a circle of radius 4000.m. a) Find the centripetal acceleration and the centripetal force acting on the pilot. b) What is the pilot's apparent weight at the bottom of the dive?
A ball that has a mass of 1.00 kg is attached to a string 1.00 m long and is whirled in a vertical circle at a constant speed of 10.0 m/s.a) Determine the tension in the string when the ball is at the top of the circle.b) Determine the tension in the string when the ball is at the bottom of the
A girl on a merry-go-round platform holds a pendulum in her hand. The pendulum is 6.00 m from the rotation axis of the platform. The rotational speed of the platform is 0.0200rev/s. It is found that the pendulum hangs at an angle 0 to the vertical. Find θ.
A flywheel of radius 31.59 cm is rotating at a constant frequency. The centripetal acceleration at a point on the edge of the flywheel is 8.629-104 m/s2. What is the frequency of rotation of the flywheel (in rpm)?
What happens to a double-slit interference pattern if a) The wavelength is increased? b) The separation between the slits is increased? c) The experimental apparatus is placed in water?
Estimate the frequency of an ultrasonic (sound) wave for which diffraction effects would be as small as they are for visible light.
Why are radio telescopes so much larger than optical telescopes? Does an X-ray telescope also have to be larger than an optical telescope?
Can light pass through a single slit narrower than its wavelength? If not, why not? If so, describe the distribution of the light beyond the slit.
One type of hologram consists of bright and dark fringes produced on photographic film by interfering laser beams. If the hologram is illuminated with white light, the image will be reproduced multiple times, in different pure colors at different sizes. a) Explain why. b) Which colors correspond to
In a single-slit diffraction pattern, there is a bright central maximum surrounded by successively dimmer higher-order maxima. Farther away from the central maximum, eventually no more maxima are observed. Is this because the remaining maxima are too dim? Or is there an upper limit to the number of
Which close pair of stars will be more easily resolvable with a telescope: two red stars or two blue ones? Assume the binary star systems are the same distance from Earth and are separated by the same angle.
A red laser pointer shines on a diffraction grating, producing a diffraction pattern on a screen behind the grating. If the red laser pointer is replaced with a green laser pointer, will the green bright spots on the screen be closer together or farther apart than the red bright spots were?
A helium-neon (He-Ne) laser has a wavelength of 632.8 nm. a) What is the wavelength of this light as it passes through Lucite with index of refraction n = 1.500? b) What is the speed of the light in the Lucite?
It is common knowledge that the visible light spectrum extends approximately from 400 nm to 700 nm. Roughly, 400 nm to 500 nm corresponds to blue light, 500 nm to 550 nm corresponds to green, 550 nm to 600 nm to yellow-orange, and above 600 nm to red. In an experiment, red light with a wavelength
What minimum path length difference is needed to cause a phase shift of π/4 in light of wavelength 700.nm?
Coherent, monochromatic light of wavelength 450.0 nm is emitted from two locations and detected at another location. The path length difference between the two routes taken by the light is 20.25 cm. Will the two light waves interfere destructively or constructively at the detection point?
A Young's double-slit experiment is performed with monochromatic green light (λ = 540 nm). The separation between the slits is 0.100 mm, and the interference pattern on a screen has the first side maximum 5.40 mm from the center of the pattern. How far away from the slits is the screen?
For a double-slit experiment, two 1.50-mm-wide slits are separated by a distance of 1.00 mm. The slits are illuminated by laser light with wavelength 633 nm. If a screen is placed 5.00 m away from the slits, determine the separation of the bright fringes on the screen.
Coherent monochromatic light with wavelength Î» = 514 nm is incident on two thin slits that are separated by a distance d = 0.500 mm. The intensity of the radiation at a screen 2.50 m away is 180.0 W/cm2. Determine the position y1/3 at which the intensity at the central peak (at y = 0) drops to
In a double-slit experiment, He-Ne laser light of wavelength 633 nm produced an interference pattern on a screen placed some distance from the slits. When one of the slits was covered with a thin glass slide of thickness 12.0 Î¼m, the central bright fringe shifted to the point occupied
Suppose the thickness of a thin soap film (n = 1.32) surrounded by air is non uniform and gradually tapers. Monochromatic light of wavelength 550 nm illuminates the film. At the thinnest end, a dark fringe is observed. How thick is the film at the two dark fringes closest to that fringe?

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