Practice Problems for Test 1

1. Fred finds an old, deflated weather balloon in a box. The box says that it will expand to a sphere d = 15 feet in diameter.
   1. If Fred inflates the balloon fully, what will its volume be? Express your result in cubic meters.
   2. The empty balloon skin has a mass of 3 kg. After Fred has inflated it, what will its total mass be?
   3. Fred is an ordinary human being. Estimate how long it will take to inflate the balloon by blowing into it.

2. The position of an electron as a function of time is given by the equation

            x(t)  =  15 m  +   (4.5 m/s) * t   -  (2.3 m/s^2) * t^2
   

   where positive values of x are to the right.
   1. What is the position of the electron at t = 6 s?
   2. What is the velocity of the electron at t = 6 s?
   3. What is the acceleration of the electron at t = 6 s?
   4. Which way is the electron moving at t = 3.6 s?
   5. At what time will the electron be at position x = 0 m?

3. Pam is standing on a balcony, H = 20 m above the ground. As she leans over the edge of the balcony, she tosses an apple upwards at v = 18 m/s.
   1. When will the apple pass Pam on its way downwards?
   2. When will the apple strike the ground?
   3. How fast will the apple be moving when it strikes the ground?

4. Tom stands at the top of a long hill with a uniform slope. He places a ball carefully on the ground, holds it still for moment, then releases it. Tom estimates that it rolls x = 52 +/- 3 cm in t = 10 s. The entire slope is L = 300 m long. Tom wonders how long it till take the ball to roll all the way down the hill.
   1. What is the percentage uncertainty in Tom's estimate of the distance rolled in 10 seconds?
   2. How long should it take the ball to roll from the top to the bottom of the hill? Give a single value here ...
   3. What are reasonable limits on your answer to part b? In other words, what are the minimum and maximum times the ball might take to roll to the bottom of the hill?