Falling Body Problems:
1. A ball with mass 0.1 kg is thrown upward with an initial velocity 20
m/s from the roof of a building 25 m high. Neglect air resistance.
(a) Find the maximum height above the ground that the ball
reaches.
(b) Find the time that it hits the ground assuming the ball
misses the building on its way down.
2. A 10 kg object is shot straight up with an initial velocity of 10 m/s from a cliff that is 60 meters high. If air
resistance is given by 2|v|, determine the velocity of the object when it
hits the ground.
3. A 5 kg object is shot straight up with an initial velocity of 10 m/s off a cliff that is 40 meters high. If air resistance is given by 2|v|, determine the maximum height the object reaches.
4. A sky diver weighing 180 lb (including equipment) falls
vertically downward from an altitude of 8000 feet and opens the
parachute after 15 seconds of free fall. Assume that the force of air
resistance is \(0.8|v|\) when the parachute is closed and \( 10|v|\)
when the parachute is open, where \(v\) is measured in ft/sec.
(a) Find the speed of the sky diver when the parachute opens.
(b) Find the distance fallen before the parachute opens.
(c) What is the limiting velocity, \(v_L\) after the parachute
opens?
(d) Determine how long the sky diver is in the air after the
parachute opens.