Solution to Exercise 1

1. The acceleration due to gravity at Earth's surface is 9.8 m/sec2 (32 ft/sec2). At the end of one second, the ball is traveling at 32 ft/sec; at the end of 2 seconds at 64 ft/sec and at the end of 3 seconds at 96 ft/sec. By 5 seconds it is (5 sec) x g = 160 ft/sec or 49 meters/sec. How far will the ball fall in this time? The distance for a falling accelerating object is given by d = 1/2 gt2. For a time of 5 seconds d = 400 ft.

2. The surface gravity on the Moon is 1/6 of its value on Earth's suface. The astronaut should be able to jump 6 times higher, or 15 feet, on the Moon.

3. Use Newton's generalization of Kepler's third law:

P2 = (4 (pi)2 / GM) R3
or
M = (4 (pi)2 R3) / (G P2)
where R = 1.88 x 10? km. Convert 16.7 days to seconds. Mass of Jupiter = 1.9 x 1027 kilogram.