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physics
mechanics

Questions and Answers of Mechanics

Cliff Height you are climbing in the High Sierra where you suddenly find yourself at the edge of a fog-shrouded cliff. To find the height of this cliff, you drop a rock from the top and 10.0 s later
Falling Can a painter is standing on scaffolding that is raised at constant speed. As he travels upward, he accidentally nudges a paint can off the scaffolding and it falls 15.0 m to the ground. You
Determined to test the law of gravity for himself a student walks off a skyscraper 180 m high, stopwatch in hand, and starts his free fall (zero initial velocity). Five seconds later, Superman
During launches, rockets often discard unneeded parts. A certain rocket starts from rest on the launch pad and accelerates upward at a steady 3.30 cm/g. When it is 235 m above the launch pad, it
A ball is thrown straight up from the ground with speed v0 At the same instant, a second ball is dropped from rest from a height H, directly above the point where the first ball was thrown upward.
Two cars, A and B, travel in a straight line. The distance of A from the starting point is given as a function of time by >At) = at + pt, with a = 2.60 m/s and p = 1.20 m/s. The distance of B from
An apple drops from the tree and falls freely. The apple is originally at rest a height H above the top of the grass of a thick lawn, which is made of blades of grass of height h. When the apple
Catching the Bus a student is running at her top speed of 5.0 m/s to catch a bus, which is stopped at the bus stop. When the student is still 40.0 m from the bus, it starts to pull away, moving with
In the vertical jump, an athlete starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00 s in the air (their "hang time"). Treat the
A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof 1.00 s later. You may ignore air resistance. (a) If the height of the building is 20.0
An alert hiker sees a boulder fall from the top of a distant cliff and notes that it takes 1.30 s for the boulder to fall the last third of the way to the ground. You may ignore air resistance. (a)
A squirrel has x- and y-coordinates (l. l m, 3.4 m) at time I, = 0 and coordinates (5.3 m, -0.5 m) at time 12 = 3.0 s. For this time interval, find (a) The components of the average velocity, and
A rhinoceros is at the origin of coordinates at time I, = O. For the time interval from I, = 0 to 12 = 12.0 s, the rhino's average velocity has x-component -3.8 m/s and y-component 4.9 m/s. At time
A web page designer creates an animation in which a dot on a computer screen has a position of r = [4.0 cm + (2.5 cm/s2)t2]i + (5.0 cm/s)tj. (a) Find the magnitude and direction of the dot's
If r = bt2i + Ct3j, where b and c are positive constants, when does the velocity vector make an angle of 45.00 with the x and y- axes?
A jet plane is flying at a constant altitude. At time I, = 0 it has components of velocity v, = 90 m/s Vy = 110 m/s. At time 12 = 30.0s the components are v, = -170m/s, Vy = 40m/s. (a) Sketch the
A dog running in an open field has components of velocity v, = 2.6 m/s and Vy = -1.8 m/s at t, = 10.0 s. For the time interval from f, = 10.0 s to 12 = 20.0 s, the average acceleration of the dog has
The coordinates of a bird flying in the xy-plane are given by X (f) = at and y (l) = 3.0m - /312, where a = 2.4m/s and J3 = 1.2 m/s2 (a) Sketch the path of the bird between t = 0 and I = 2.0 s.
A particle moves along a path as shown in Fig. 3.38. Between points B and D, the path is a straight line. Sketch the acceleration vectors at A, C, and E in the cases in which (a) The particle moves
A physics book slides off a horizontal tabletop with a speed of 1.10 m/s. It strikes the floor in 0.350 s. Ignore air resistance. Find (a) The height of the tabletop above the floor; (b) The
A military helicopter on a training mission is flying horizontally at a speed of 60.0 m/s and accidentally drops a bomb (fortunately not armed) at an elevation of 300 m. You can ignore air
Two crickets, Chirpy and Milada, jump from the top of a vertical cliff. Chirpy just drops and reaches the ground in 3.50 s, while Milada jumps horizontally with an initial speed of 95.0 cm/s. How far
A daring 510-N swimmer dives off a cliff with a running horizontal leap, as shown in Fig. 3.39. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge
Leaping the River I.A car comes to a bridge during a storm and finds the bridge washed out. The driver must get to the other side, so he decides to try leaping it with his car. The side of the road
A small marble rolls horizontally with speed Vo off the top of a platform 2.75 m tall and feels no appreciable air resistance. On the level ground, 2.00 m from the base of the platform, there is a
Inside a starship at rest on the earth, a ball rolls off the top of a horizontal table and lands a distance D from the foot of the table. This starship now lands on the unexplored Planet X. The
A rookie quarterback throws a football with an initial upward velocity component of 16.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (a) How much time is required
On level ground a shell is fired with an initial velocity of 80.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (a) Find the horizontal and vertical components of the
A pistol that fires a signal flare gives it an initial velocity (muzzle velocity) of 125 m/s at an angle of 55.0° above the horizontal. You can ignore air resistance. Find the flare's maximum height
A major leaguer hits a baseball so that it leaves the bat at a speed of30.0 m/s and at an angle of36.9" above the horizontal. You can ignore air resistance. (a) At what two times is the baseball at a
A shot putter releases the shot some distance above the level ground with a velocity of 12.0 m/s, 51.00 above the horizontal. The shot hits the ground 2.08 s later. You can ignore air resistance.
Win the Prize. In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal
Suppose the departure angle Uo in Fig. 3.26 is 42.0° and the distance d is 3.00 m. Where will the dart and monkey meet if the initial speed of the dart is (a) 12.0 m/s (b) 8.0m/s (c) What will
A man stands on the roof of a 15.0-m-tall building and throws a rock with a velocity of magnitude 30.0 m/s at an angle of 33.0° above the horizontal. You can ignore air resistance. Calculate (a)
Firemen are shooting a stream of water at a burning building using a high-pressure hose that shoots out the water with a speed of 25.0 m/s as it leaves the end of the hose. Once it leaves the hose,
A 124-kg balloon carrying a 22-1
A cannon located 60.0 m from the base of a vertical 25.O-mtall cliff, shoots a 15-kg shell at 43.0 o above the horizontal toward the cliff. (a) What must the minimum muzzle velocity be for the
An airplane is flying with a velocity of 90.0 m/s at an angle of 23.0o above the horizontal. When the plane is 114 m directly above a dog that is standing on level ground, a suitcase drops out of the
On your first day at work for an appliance manufacturer, you are told to figure out what to do to the period of rotation during a washer spin cycle to triple the centripetal acceleration. You impress
The earth has a radius of 6380 km and turns around once 011 its axis in 24 h. (a) What is the radial acceleration of an object at the earth’s equator? Give your answer in m/s2, and as a fraction
A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min (a) What is the linear speed of the
In a test of a "g-suit," a volunteer is rotated in a horizontal circle of radius 7.0 m. What must the period of rotation be so that the centripetal acceleration has a magnitude of (a) 3.0g? (b) 109?
The radius of the earth's orbit around the sun (assumed to be circular) is 1.50 X 108 km, and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of
A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center (Fig. 3.42). The linear speed of a passenger on the rim is constant and equal to 7.00 m/s. What are the
The Ferris wheel in Fig. 3.42, which rotates counterclockwise, is just starting up. At a given instant, a passenger on the rim of the wheel and passing through the lowest point of his circular motion
Hyper gravity at its Ames Research Center, NASA uses its large ''2().G" centrifuge to test the effects of very large accelerations (''hyper gravity'') on test pilots and astronauts. In this device,
A railroad flatcar is traveling to the right at a speed of 13.0 m/s relative to an observer standing on the ground. Someone is riding a motor scooter on the flatcar (Fig. 3.43). What is the velocity
A ''moving sidewalk" in an airport terminal building moves at 1.0 m/s and is 35.0 m long. If a woman steps on at one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does she
Two piers, A and B, are located on a river: B is 1500 m downstream from A (Fig. 3.44). Two friends must make round trips from pier A to pier B and return. One rows a boat at a constant speed of 4.00
A canoe has a velocity of 0.40 m/s southeast relative to the earth. The canoe is on a river that is flowing 0.50 m/s east relative to the earth find the velocity (magnitude and direction) of the
An airplane pilot wishes to fly due west. A wind of80.0 km/h (about 50 mi/h) is blowing toward the south. (a) If the airspeed of the plane (its speed in still air) is 320.0 km/h (about 200 mi/h),
Crossing the River I A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.2 m/s due east. The river is 800 m wide. (a)
Crossing the River II (a) In which direction should the motorboat in Exercise 3.41 head in order to reach a point on the opposite bank directly east from the starting point? (The boat's speed
The nose of an ultra light plane is pointed south, and its airspeed indicator shows 35 m/s. The plane is in a 10-m/s wind blowing toward the southwest relative to the earth. (a) In a
A faulty model rocket moves in the xy-plane (the positive y direction is vertically upward). The rocket's acceleration has components ax (t) = at2 and ay (t) = B - yt where a = 2.50 m/s4, B = 9.00
A rocket is fired at an angle from the top of a tower of height ho = 50.0 m. Because of the design of the engines, its position coordinates are of the form x(t) = A + Bt2 and y(t) = C + Dt3 where A,
A bird flies in the xy-plane with a velocity vector given by v = (a - Pt2) i + -ytj, with a = 2.4 m/s, p = 1.6 m/S3, and -y = 4.0m/S2. The positive y-direction is vertically upward at t = 0 the bird
A test rocket is launched by accelerating it along a 200.0-m incline at 1.25 m/s2 starting from rest at point A (Figure 3.45.) The incline rises at 35.0o above the horizontal, and at the instant the
Martian Athletics in the long jump, an athlete launches herself at an angle above the ground and lands at the same height, trying to travel the greatest horizontal distance. Suppose that on earth she
Dynamite! A demolition crew uses dynamite to blow an old building apart. Debris from the explosion flies off in all directions and is later found at distances as far as 50 m from the explosion.
Spiraling up it is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant
A jungle veterinarian with a blow-gun loaded with a tranquilizer dart and a sly 1.5-kg monkey are each 25 m above the ground in trees 90 m apart. Just as the hunter shoots horizontally at the monkey,
A movie stuntwoman drops from a helicopter that is 30.0 m above the ground and moving with a constant velocity whose components are 10.0 m/s upward and 15.0 m/s horizontal and toward the south. You
In fighting forest fires, airplanes work in support of ground crews by dropping water on the fires. A pilot is practicing by dropping a canister of red dye, hoping to hit a target on the ground
As a ship is approaching the dock at 45.0 cm/s, an important piece of landing equipment needs to be thrown to it before it can dock. This equipment is thrown at 15.0 m/s at 60.00 above the horizontal
The Longest Home Run according to the Guinness Book of World Records, the longest home run ever measured was hit by Roy "Dizzy" Carlyle in a minor league game. The ball traveled 188 m (618 ft) before
A water hose is used to fill a large cylindrical storage tank of diameter D and height W. The hose shoots the water at 45° above the horizontal from the same level as the base of the tank and is
A projectile is being launched from ground level with no air resistance. You want to avoid having it enter a temperature inversion layer in the atmosphere a height h above the ground. (a) What is
Kicking a Field Goal in U.S. football, after a touchdown the team has the opportunity to earn one more point by kicking the ball over the bar between the goal posts. The bar is 10.0 ft above the
A projectile is launched with speed Vo at an angle ao above the horizontal. The launch point is a height h above the ground. (a) Show that if air resistance is ignored, the horizontal distance that
Look Out A snowball rolls off a barn roof that slopes downward at an angle of 40" (Fig. 3.49). The edge of the roof is 14.0 m above the ground, and the snowball has a speed of 7.00 m/s as it rolls
(a) Prove that a projectile launched at angle ao has the same horizontal range as one launched with the same speed at angle (90o - ao). (b) A frog jumps at as peed of22 m/s and lands 25 cm from its
On the Flying Trapeze, A new circus act is called the Texas Tumblers Lovely Mary Belle swings from a trapeze, projects herself at an angle of 53o, and is supposed to be caught by Joe Bob, whose hands
A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle (Fig. 3.51). The takeoff ramp was inclined at 53.0", the river was
A rock is thrown from the roof of a building with a velocity Vo at an angle of ao from the horizontal. The building has height h. You can ignore air resistance. Calculate the magnitude of the
A 5500-kg cart carrying a vertical rocket launcher moves to the right at a constant speed of 30.0 m/s along a horizontal track. It launches a 45.O-kg rocket vertically upward with an initial speed of
A 2.7-kg ball is thrown upward with an initial speed of 20.0 m/s from the edge of a 45.O-m-high cliff. At the instant the ball is thrown, a woman starts running away from the base of the cliff with a
A 76.O-kg boulder is rolling horizontally at the top of a vertical cliff that is 20 m above the surface of a lake, as shown in Fig. 3.52. The top of the vertical face of a dam is located 100 m from
Tossing Your Lunch Henrietta is going off to her physics class, jogging down the sidewalk at 3.05 m/s. Her husband Bruce suddenly realizes that she left in such a hurry that she forgot her lunch of
Two tanks are engaged in a training exercise on level ground. 1bc first tank fires a paint-filled training round with a muzzle speed of 250 m/s at 10.0° above the horizontal while advancing toward
Bang! A student sits atop a platform a distance h above the ground. He throws a large firecracker horizontally with a speed v. However, a wind blowing parallel to the ground gives the firecracker a
A rocket is launched vertically from rest with a constant upward acceleration of 1.75 m/s'. Suddenly 220 s after launch, an unneeded fuel tank is jettisoned by shooting it away from the rocket. A
When it is 145 m above the ground, a rocket traveling vertically upward at a constant 8.50 m/s relative to the ground launches a secondary rocket a! a speed of 12.0 m/s at an angle of 53.0° above
In a Fourth of July celebration, a firecracker is launched from ground level with an initial velocity of 25.0 m/s a! 30.00 From the vertical. At its maximum height it explodes in a starburst into
In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 90.0 km/h, to his enemy's car, which is going 110 km/h. The enemy's car is 15.8 m in front of the
A rock tied to a rope moves in the xy-plane. Its coordinates are given as functions of time by s(t) = R cos wt y(t) = R sin wt where R and", are constants. (a) Show that the rock's distance from
A 400.0-m-wide river flows from west to east at 30.0 m/min. Your boat moves at 100.0 m/min relative to the water no matter which direction you point it. To cross this river, you start from a dock at
A particle moves in the xy-plane. Its coordinates are given as functions of time by x(t) = R (wt – sin wt) y(t) = R (1 – cos wt) where Rand", are constants. (a) Sketch the trajectory of the
A projectile is fired from point A at an angle above the horizontal. At its highest point, after having traveled a horizontal distance D from its launch point, it suddenly explodes into two identical
Centrifuge on Mercury. A laboratory centrifuge on earth makes n rpm (rev/min) and produces an acceleration of 5.00g at its outer end. (a) What is the acceleration ("m g's) at a point halfway out to
Raindrops when a train's velocity is 120 m/s eastward, raindrops that are falling vertically with respect to the earth make traces that are inclined 30.00 to the vertical on the windows of the
An airplane pilot sets a compass course due west and maintains an airspeed of 220 km/h. After flying for 0.500 h, she finds herself over a town 120 km west and 20 km south of her starting point.
An elevator is moving upward at a constant speed of 2.50 m/s. A bolt in the elevator ceiling 3.00 m above the elevator floor works loose and falls. (a) How long does it take for the bolt to fall to
Suppose the elevator in Problem 3.82 starts from rest and maintains a constant upward acceleration of 4.00 m/s2, and the bolt falls out the instant the elevator begins to move. (a) How long does it
City A lies directly west of city B When there is no wind an airliner makes the 5550-kInround-trlp flight between them in 6.60h of flying time while traveling at the same speed in both directions.
In a World Cup soccer match, Juan is running due north toward the goal with a speed of 8.00 m/s relative to the ground. A teammate passes the ball to him. The ball has a speed of 12.0 m/s and is
A man is riding on a flatcar traveling at a constant speed of 9.10 m/s (Fig. 3.54). He wishes to throw a ball through a stationary hoop 4.90 m above the height of his hands in such a manner that the
A shotgun fires a large number of pellets upward, with some pellets traveling very nearly vertically and others as much as 1.00 from the vertical. Assume that the initial speed of the pellets is
A projectile is thrown from a point P. It moves in such a way that its distance from P is always increasing. Find the maximum angle above the horizontal with which the projectile could have been
Projectile Motion on an inline I, a baseball is given an initial velocity with magnitude Vo at an angle Φ above the surface of an incline, which is in turn inclined at an angle e above the

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