Chapter 2

A rocket-driven sled running on a straight, levcl track is used to investigate the effects of large accelerations on humans. One such sled can attain a speed of \(1600 \mathrm{~km} / \mathrm{h}\) in \(1.8 \mathrm{~s}\), starting from rest. Find (a) the acceleration (assumed constant) in terms of \(g\) and (b) the distance traveled.

A motorcyclist who is moving along an \(x\) axis directed toward the east has an acceleration given by \(a=(6.1-1.2 t) \mathrm{m} / \mathrm{s}^{2}\) for \(0 \leq t \leq 6.0 \mathrm{~s}\). At \(t=0,\) the velocity and position of the cyclist are \(2.7 \mathrm{~m} / \mathrm{s}\) and \(7.3 \mathrm{~m}\). (a) What is the maximum speed achieved by the cyclist? (b) What total distance does the cyclist travel between \(t=0\) and \(6.0 \mathrm{~s} ?\)

A car moving with constant acceleration covered the distance between two points \(60.0 \mathrm{~m}\) apart in \(6.00 \mathrm{~s}\). Its speed as it passed the second point was \(15.0 \mathrm{~m} / \mathrm{s}\). (a) What was the speed at the first point? (b) What was the magnitude of the acceleration? (c) At what prior distance from the first point was the car at rest? (d) Graph \(x\) versus \(t\) and \(v\) versus \(i\) for the car, from rest \((t=0)\)

A certain juggler usually tosses halls vertically to a height \(H\). To what height must they be tossed if they are to spend twice as much time in the air?

\(A\) rock is dropped from a \(100-\mathrm{m}\) -high cliff. How long does it take to fall (a) the first \(50 \mathrm{~m}\) and (b) the second \(50 \mathrm{~m}\) ?

Two subway stops are separated by \(1100 \mathrm{~m}\). If a subway train accelerates at \(+1.2 \mathrm{~m} / \mathrm{s}^{2}\) from rest through the first hall of the distance and decelerates at \(-1.2 \mathrm{~m} / \mathrm{s}^{2}\) through the second half, what are (a) its travel time and (b) its maximum speed? (c) Graph \(x, v\) and \(a\) versus \(t\) for the trip.

A stone is thrown vertically upward. On its way up it passes point \(A\) with speed \(v\), and point \(B, 3.00 \mathrm{~m}\) higher than \(A,\) with speed \(\frac{1}{2} v .\) Calculate (a) the speed \(v\) and (b) the maximum height reached by the stone above point \(B\).

A rock is dropped (from rest) from the top of a \(60-\mathrm{m}\) -tall building. How far above the ground is the rock \(1.2 \mathrm{~s}\) before it reaches the ground?

A lead ball is dropped in a lake from a diving board \(5.20 \mathrm{~m}\) ahove the water. It hits the water with a certain velocity and then sinks to the bottom with this same constant velocity. It reaches the bottom \(4.80 \mathrm{~s}\) after it is dropped. (a) How deep is the lake? What are the (b) magnitude and (c) direction (up or down) of the average velocity of the ball for the entire fall? Suppose that all the water is drained from the lake. The ball is now thrown from the diving board so that it again reaches the bottom in \(4.80 \mathrm{~s}\). What are the (d) magnitude and (e) direction of the initial velocity of the ball?

The single cable supporting an unocceupied construction evator breaks when the elevator is at rest at the top of a \(120-\mathrm{m}\) -high building. (a) With what speed does the elevator strike the ground? (b) How long is it falling? (c) What is its speed when it passes the halfway point on the way down? (d) How long has it been falling when it passes the halfway point?

A ball is thrown vertically downward from the top of a \(36.6-\mathrm{m}\) -tall building. The ball passes the top of a window that is \(12.2 \mathrm{~m}\) above the ground \(2.00 \mathrm{~s}\) after heing thrown. What is the specd of the ball as it passes the top of the window?

A parachutist bails out and freely falls \(50 \mathrm{~m}\). Then the parachute opens, and thercafter she decclerates at \(2.0 \mathrm{~m} / \mathrm{s}^{2} .\) She reaches the ground with a speed of \(3.0 \mathrm{~m} / \mathrm{s}\). (a) How long is the parachutist in the air? (b) At what height does the fall begin?

A ball is thrown down vertically with an initial speed of \(v_{0}\) from a height of \(h\). (a) What is its speed just before it strikes the ground? (b) How long does the ball take to reach the ground? What would be the answers to (c) part a and (d) part b if the ball were thrown upward from the same height and with the same initial speed? Before solving any equations, decide whether the answers to (c) and (d) should be greater than, less than, or the same as in (a) and (b).

The sport with the fastest moving ball is jai alai, where measured speeds have reached \(303 \mathrm{~km} / \mathrm{h}\). If a professional jai alai player faces a ball at that speed and involuntarily blinks, he blacks out the scene for \(100 \mathrm{~ms}\). How far does the ball move during the blackout?

If a baseball pitcher throws a fastball at a horizontal speed of \(160 \mathrm{~km} / \mathrm{h},\) how long does the ball take to reach home plate \(18.4 \mathrm{~m}\) away?

A motorcycle is moving at \(30 \mathrm{~m} / \mathrm{s}\) when the rider applies the brakes, giving the motorcycle a constant deceleration. During the \(3.0 \mathrm{~s}\) interval immediately after braking begins, the speed decreases to \(15 \mathrm{~m} / \mathrm{s} .\) What distance does the motorcycle travel from the instant braking begins until the motorcycle stops?

A shuffleboard disk is accelerated at a constant rate from rest to a speed of \(6.0 \mathrm{~m} / \mathrm{s}\) over a \(1.8 \mathrm{~m}\) distance by a player using a cue. At this point the disk loses contact with the cue and slows at a constant rate of \(2.5 \mathrm{~m} / \mathrm{s}^{2}\) until it stops. (a) How much time elapses from when the disk begins to accelerate until it stops? (b) What total distance does the disk travel?

The head of a rattlesnake can accelerate at \(50 \mathrm{~m} / \mathrm{s}^{2}\) in striking a victim. If a car could do as well, how long would it take to reach a speed of \(100 \mathrm{~km} / \mathrm{h}\) from rest?

A jumbo jet must reach a speed of \(360 \mathrm{~km} / \mathrm{h}\) on the runway for takcoff. What is the lowest constant accelcration needed for takcoff from a \(1.80 \mathrm{~km}\) runway?

An automobile driver increases the speed at a constant rate from \(25 \mathrm{~km}\) 'h to \(55 \mathrm{~km} / \mathrm{h}\) in \(0.50 \mathrm{~min}\). A bicycle rider speeds up at a constant rate from rest to \(30 \mathrm{~km} / \mathrm{h}\) in \(0.50 \mathrm{~min}\). What are the magnitudcs of (a) the driver's acceleration and (b) the rider's acceleration?

On average, an eye blink lasts about \(100 \mathrm{~ms}\). How far does a MiG-25 "Foxhat" fighter travel during a pilot's blink if the planc's average vclocity is \(3400 \mathrm{~km} / \mathrm{h} ?\)

A certain sprinter has a top speed of \(11.0 \mathrm{~m} / \mathrm{s}\). If the sprinter starts from rest and accelerates at a constant rate, he is able to reach his top speed in a distance of \(12.0 \mathrm{~m}\). He is then able to maintain this top speed for the remainder of a \(100 \mathrm{~m}\) race. (a) What is his time for the \(100 \mathrm{~m}\) race? (b) In order to improve his time, the sprinter trics to decrease the distance required for him to reach his top speed. What must this distance be if he is to achieve a time of \(10.0 \mathrm{~s}\) for the race?

The speed of a bullet is measured to be \(640 \mathrm{~m} / \mathrm{s}\) as the bullct cmerges from a barrel of length \(1.20 \mathrm{~m}\). A ssuming constant accelcration, find the time that the bullet spends in the barrel after it is fired.

The Zero Gravity Research Facility at the NASA Glenn Research Center includes a 145 m drop tower. This is an evacuated vertical tower through which, among other possibilities, a 1 -m-diameter sphere containing an experimental package can he dropped. (a) How long is the sphere in free fall? (b) What is its speed just as it reaches a catching device at the bottom of the tower? (c) When caught, the sphere experiences an average deceleration of \(25 \mathrm{~g}\) as its speed is reduced to zero. Through what distance does it travel during the deceleration?

A car can be braked to a stop from the autobahn-like speed of \(200 \mathrm{~km} / \mathrm{h}\) in \(170 \mathrm{~m}\). Assuming the acceleration is constant, Find its magnitude in (a) SI units and (b) in terms of g. (c) How much time \(T_{b}\) is required for the braking? Your reaction time \(T,\) is the time you require to perceive an emergency, move your foot to the brake. and begin the braking. If \(T_{r}=400 \mathrm{~ms}\), then (d) what is \(T_{b}\) in terms of \(T_{n}\) and \((\mathrm{c})\) is most of the full time required to stop spent in reacting or braking" Dark sunglasses delay the visual signals sent from the cyes to the visual cortex in the brain, increasing \(T_{r-}\) (f) In the extreme case in which \(T_{r}\) is increased by \(100 \mathrm{~ms}\), how much farther does the car travel during your reaction time?

In \(1889,\) at Jubbulpore, India, a tug-of-war was finally won after \(2 \mathrm{~h} 41 \mathrm{~min},\) with the winning team displacing the center of the rope \(3.7 \mathrm{~m} .\) In centimeters per minute, what was the magnitude of the average velocity of that center point during the contest?

Most important in an investigation of an airplane crash by the U.S. National Transportation Safety Board is the data stored on the airplane's flight-data recorder, commonly called the "black box" in spite of its orange coloring and reflective tape. The recorder is engineered to withstand a crash with an average deceleration of magnitude \(3400 \mathrm{~g}\) during a time interval of \(6.50 \mathrm{~ms}\). In such a crash, if the recorder and airplane have zero speed at the end of that time interval, what is their speed at the beginning of the interval?

From January \(26,1977,\) to September \(18,1983,\) George Meegan of Great Britain walked from Ushuaia, at the southern tip of South America, to Prudhoe Bay in Alaska, covering \(30600 \mathrm{~km}\). In meters per second, what was the magnitude of his average velocity during that time period?

The wings on a stoncfly do not flap, and thus the insect cannot fly. However, when the insect is on a water surface, it can sail across the surface by lifting its wings into a hreere. Suppose that you time stoneflies as they move at constant speed along a straight path of a certain length. On average, the trips each take \(7.1 \mathrm{~s}\) with the wings set as sails and \(25.0 \mathrm{~s}\) with the wings tucked in. (a) What is the ratio of the sailing speed \(v_{s}\) to the nonsailing speed \(v_{\sin } ?\) (b) In terms of \(v_{s .}\) what is the difference in the times the inscets take to travel the first \(2.0 \mathrm{~m}\) along the path with and without sailing?

The position of a particle as it moves along a \(y\) axis is given by $$ y=(2.0 \mathrm{~cm}) \sin (\pi t / 4) $$ with \(t\) in seconds and \(y\) in centimeters. (a) What is the average velocity of the particle between \(t=0\) and \(t=2.0 \mathrm{~s} ?\) (b) What is the instantaneous velocity of the particle at \(t=0,1.0,\) and \(2.0 \mathrm{~s} ?\) (c) What is the average acceleration of the particle between \(t=0\) and \(t=2.0 \mathrm{~s} ?\) (d) What is the instantancous acceleration of the particle at \(t=0\), \(1.0,\) and \(2.0 \mathrm{~s} ?\)