1.A bicyclist is finishing his repair of a flat tire when a friend rides by with
ID: 2138510 • Letter: 1
Question
1.A bicyclist is finishing his repair of a flat tire when a friend rides by with a constant speed of 3.4 m/s. Two seconds later the bicyclist hops on his bike and accelerates at 2.0 m/s2 until he catches his friend. (a) How much time does it take until he catches his friend? (b) How far has he traveled in this time? (c) What is his speed when he catches up? 2.An arrow is fired with a speed of 18.0 m/s at a block of Styrofoam resting on a smooth surface. The arrow penetrates a certain distance into the block before coming to rest relative to it. During this process the arrow's deceleration has a magnitude of 1700 m/s2 and the block's acceleration has a magnitude of 450 m/s2 (a) How long does it take for the arrow to stop moving with respect to the block? (b) What is the common speed of the arrow and block when this happens? (c) How far into the block does the arrow penetrate? 3.A hot air balloon has just lifted off and is rising at the constant rate of 2.2 m/s. Suddenly, one of the passengers realizes she has left her camera on the ground. A friend picks it up and tosses it straight upward with an initial speed of 10.8 m/s. If the passenger is 2.5 m above her friend when the camera is tossed, how high is she when the camera reaches her? 4.Weights are tied to each end of a 19.0 cm string. You hold one weight in your hand, and let the other hang vertically a height h above the floor. When you release the weight in your hand, the two weights strike the ground one after the other with audible thuds. Find the value of h for which the time between release and the first thud is equal to the time between the first thud and the second thud. 5.Sitting in a second-story apartment, a physicist notices a ball moving straight upward just outside her window. The ball is visible 0.27 s as it moves a distance of 1.20 m from the bottom to the top of the window. (a) How long does it take before the ball reappears? (b) What is the greatest height of the ball above the top of the window?Explanation / Answer
1)
The distance traveled by the friend is
d= 3.4 X T
T= time to catch his friend
The distance traveled by the passed cyclist is
d= 1/2 X acceleration X t^2 = 1/2 *( 2.0)* ( T - 2 )^2
So 3.4T = 1/2 *( 2.0 )*( T-2)^2
Use the quadratic equation to solve T^2 - 7.4T + 4
T=6.66 sec
Distance= 22.64m
Speed= 22.64/10= 2.26m/s
2).
When the arrow hits the block, it is travelling at 18 m/sec. It then decelerates at 1700 m/s
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