Physics 581 Homework#1
Due Friday July 24
1. Straight line motion: sketch qualitatively how downward acceleration varies with time for:
(a) a sky diver, from plane to ground,
(b) a bungee jumper, from start to finish.
For purposes of this question, assume survival of both the above.
2. (WARNING: The only formula allowed in this question is distance = average speed x time taken, which is really just the definition of average speed. Use of any other formulas you may know will be penalized! Just think through the steps as they are given.)
Suppose you throw a ball vertically upwards at 20 meters per second, and assume the natural acceleration due to gravity is 10 meters per second per second downwards.
(a) What is the velocity of the ball after one, two, three and four seconds?
(b) How long did it take the ball to reach its highest point?
(c) What was its average speed on the way up?
(d) Using your results from (b) and (c) figure out how high it got.
(e) Suppose you throw a tennis ball at 45 degrees to the horizontal and it stays in the air four seconds. Ignoring air resistance, how far away from you does it land? (Neglect the height of your hand above the ground.) What was its speed when it left your hand?
(f) Same as (e), except now it stays in the air only two seconds. How far did you throw it? How fast did you throw it?
(g) Find out approximately how far you can throw a tennis ball, and then figure out from your results above about how fast you can throw.
3. Since the moon has no atmosphere, it is possible for a spaceship to be in orbit just a few miles above the surface (to clear the mountains) indefinitely, without needing to use fuel, once it's up to speed.
The purpose of this question is to figure out just how fast this spaceship needs to be moving to maintain this orbit. The reasoning parallels that used in the discussion of Newton's cannon on a mountain.
(a) Given that the acceleration due to gravity near the moon's surface is one-fifth of its value on earth, if you drop something while standing on the moon, how fast is it moving one second after you release it? (Give the answer in meters per second).
(Note: actually the moon's gravity is around 17% of earth's, I'm just trying to keep the figures simple.)
(b)What was its average speed during the first second of its falling?
(c) Use your answer to (b) to figure out how far it fell in the first second.
(d) Now think about the spaceship. Imagine it is initially traveling at some high speed parallel to the moon's surface, which we take to be flat at this point. For it to orbit the moon properly, the distance it falls below a straight line in one second must be just the distance the (curved) surface of the moon falls away below it over the distance the spaceship moves horizontally in one second. But we know from c) above how far it falls in one second. So, we have to figure out over what horizontal distance the moon's surface curves below a straight line by this amount. Draw a picture of a suitable triangle, with one corner at the center of the moon, to figure out how far the spaceship moves in one second.
(e) How long does the spaceship take to do one complete orbit of the moon?