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Instructions for PHY 2048 Problem Set (PSET): (1) Please NEATLY write your name and your solutions. (2) You must use blank 8x11 printer paper. (3) Begin each problem on a new page, and put your name on each page. Staple your pages together. 4) Only write on one side of the page. (5) You must write up your solutions independently (i.e. dont copy anyone elses solutions), using your own words and thought process. You must show all of your work. (6) No credit will be given for the final answer if it is not derived or explained! (7) This Problem set consists of five problems. It corresponds to the material covered in the first four chapters of the textbook. The maximum possible score for the PSET is 100 points (8) Anyone who fails to follow the PSET instruction listed above will get 50 points penalty from the Problem Set score. Helpful Tips: Its not a good idea to punch numbers into a calculator. Plugging in numbers at the very end will often save you time and mistakes.
Problem One dimensional kinematics: track event During a track event two runners, Bob, and Jim, round the last turn and head into the final stretch with Bob a distance d in front of Jim. They are both running with the same velocity %, when the finish line is a distance s away fromim, Jim accelerates at a constant a,until he catches up to Bob and passes him. Jim then continues at a constant speed until he reaches the finish line. a) How long did t take Jim to catch Bob? b) How far did Jim still have to run when he just caught up to Bob? c) How long did Jim take to reach the finish line after he just caught up to Bob? Bob starts to accelerate at a constant ag at the exact moment that Jim catches up to him, and accelerates all the way to the finish line and crosses the line exactly when Jim does. Assume Bobs acceleration is constant d) What is Bobs acceleration? e) What is Bobs velocity at the finish line? Who is running faster? Problem 2 As soon as a traffic light turns green, a car speeds up from rest to its cruising speed 22.3 m/sec with constant acceleration 4.02 m/sec2. In the adjoining bicycle lane, a cyclist speeds up from rest to its cruising speed 8.94 m/sec with constant acceleration 5.81 m/sec. Each vehicle maintains constant velocity after reaching its cruising speed. (a) For what time interval is the bicycle ahead of the car? (b) By what maximum distance does the bicycle lead the car?
Problem 3 An NBA player throws a basketball at a horizontal distance of 10.0 m from the center of the basket. The basket is at a height of 3.05 m above the floor as shown below. He shoots the ball at an angle 0-40.0 with respect to the horizontal direction and releases it at the height of 2.00 m above the floor (a) Please indicate clearly in words on the following figure for the origin of the x and y coordinates that you will set to solve this problem, b) What initial speed vo must the player throw the ball so that it goes through the center of the basket without the ball touching the rim (a swish!!)? (c) What is the maximum height with respective to the floor reached by the ball? (d) How far horizontally is the ball from the basket when the ball is at the maximum height? (e) Find the time of flight of the ball from the point it leaves the hand of the player to it reaches basket. 0.0 3.05 m 10.0 m
Problem 4 An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once be fore reaching the catcher. Assume the angle at which the bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in the figure below, but that the balls speed after the bounce is one-half of what is was before the bounce (a) Assume the ball is always thrown with the same initial speed and ignore air resistance. At what angle 0 should the fielder throw the ball to make it go the same distance D with one bounce (blue path) as a ball thrown upward at 45.0 with no bounce (green path)? (b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw 45.0 Problem 5 A water hose is used to fill a large cylindrical storage tank of diameter D and height 2D. The hose shoots the water at 45 above the horizontal from the same level as the base of the tank and is a distance 6D away. For what range of lunch speeds Vo will the water enter the tank? Ignore air resistance, and express your answer in terms of D and g. 2D Water D궈
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Answer #1

Problem 2:

Data:
Car:
Vi=0 Vf = 22.3 m/s ; a = 4.02 m/s2
Bike:
Vi=0 Vf = 8.94 m/s ; a = 5.81 m/s2

So let's calculate how long it takes the bike to reach its cruising speed.
t = (vf-vi)/a ; t = 8.94/5.81 ; t = 1.539 sec
Now let's calculate the distance it covered during that time.
d = 1/2at2 ; d = 1/2(5.81)(1.539`2) ;d = 6.88 m

Now calculate how long it took the car to reach the bike's cruising speed.
t = (vf-vi)/a ; t = 22.3/4.02 ; t = 5.55 sec
Calculate the distance traveled during this time
d = 1/2 at2 ; d = 1/2(4.02)(5.552) ;d = 61.91 m

At 1.539 sec and a distance of 6.88 m, the car is not accelerating any more so its distance from the start line can be calculated by the equation d = 8.94 t - 6.88

The distance the car travels from the start line after it reaches the bike's cruising speed is d = 8.94 t + 1/2(4.02)t2 - 61.91 since the car is still accelerating.

Since the total distances will be the same when the car catches up to the bike we substitute the first equation into the second equation.

8.94 t - 6.88 = 8.94 t + 1/2(4.02) t 2 - 61.91

Solve for t.

t = 5.23 s  which is the time from the car reaching the bike's final velocity which took 5.55 s. Add these times together
5.23 + 5.55 = 10.78 sec

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