If a boy(500N) wishes to slide down a rope that has a breaking stand of 350N, then:

Question

(a) with what acceleration must it move downward in order to not break the rope.
(b) if he slide 30m, how long will it take?
(c) how fast will he be going before he hits the ground?

Answer 1

Force up on boy = rope tension T
Force down on boy = m g
acceleration of boy downward = a
then
ma = mg - T
here m = 500/9.81 = 50.97 kg
so
50.97 a = 500 - 350 = 150
a = 150/50.97 = 2.94 m/s^2

d = (1/2) a t^2
30 = 1.47 t^2
t = 4.52 seconds

assuming 30 meters is the ground then
v = a t = 2.94 * 4.52

Answer 2

Now your elevator problem and your rope problem are very much the same so look them over carefully.