1.7 m long pendulum is setup from a 3 m ceiling so that it is at its peak (h=.65 m), it is then released. At the bottom of the swing the string is cut (assume no engery loss during the cutting process)

Question

1.) what is vertical velocity right before it hits the ground?
2.) how far does the pendulum bob travel away from the pendulum before it hits the ground?
3.) An 80.kg climber with a 20.0 kg pack climbs 8848 m to the t?op of mount everest. how much work did the climber exert in the climbing the mountain

Answer 1

When the string is cut, the bob has only horizontal velocity u. It keeps that horizontal velocity u until it hits the ground because there is no horizontal force after that.
So there are two separate problems here:
1. How far does it go at constant speed u for time t?
2. If you drop it from 3-1.7 = 1.3
meters high, how fast does it hit the ground and how long does it take, time t?
Problem 1:
(1/2)m u^2 = m g h
h = .65 m so
u = sqrt (2*9.81*.65) = 3.57 m/s for time t, the falling time
Problem 2:
Vi = 0 downward
(1/2) m v^2 = m g (1.3)
v^2 = 2 * 9.81 * 1.3
v = 5.05 m/s (That is the answer to part 1)
average speed down = (0+5.05)/2 = 2.53 m/s
so fall time t = 1.3/2.53 = .515 s
then from the horizontal problem
d = u t = 3.57 * .515 = .84 meters

Answer 2

3.) An 80.kg climber with a 20.0 kg pack climbs 8848 m to the t?op of mount everest. how much work did the climber exert in the climbing the mountain
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100 kg up 8848 meters

100 * 9.81 * 8848 = 8,679,888 Joules

(That is the useful work, his efficiency would make it a lot worse)