Practice problem for quiz (which is Wednesday A and Thursday E) - answers below

On the quiz (Wednesday for A, Thursday for E), you will answer questions related to:  unit conversions, Fermi approximation questions, equations of motion (which will be given) and graphs of motion.  Review the previous homework and your notes.

Practice problem:

This problem assumes that the acceleration is that of near-Earth surface gravity, 9.8 m/s/s.

Consider an ball dropped from rest, now in freefall with minimal air resistance  It is easiest to define DOWN as positive.

a.  What is the ball's speed after 2.5 seconds of fall?

b.  How far has the ball fallen in this time?

c.  Draw an approximate graph of motion for d vs. t.

d.  Draw an approximate graph of motion for v vs. t.

e.  If, after 2.5 seconds of fall. the ball hits a swimming pool that is 2-m deep with water.  Imagine that the ball slows down uniformly during its descent to the bottom finally hitting a speed of 4 m/s right before it hits bottom.  What is the ball's acceleration during this descent through water, and how long did it take to reach the bottom?

Answers:

a.  Vf = Vi + at = 0 + (9.8)2.5 = 24.5 m/s

b.  d = Vi t + 0.5 at^2 = 0 + (0.5)(9.8)(2.5^2) = 30.6 m

c.  basic parabola

d.  linear

e.  Use the 4th equation of motion for the easiest solution.

4^2 = 24.5^2 + 2 a (2)

a = -146 m/s/s

Yes, that's a pretty big deceleration, so maybe not totally realistic.

Using the first equation of motion:

Vf = Vi + at

4 = 24.5 + (-146)t

t = 0.14 sec