A rope AB attached to a small block of neglible dimensions and passes over apulley C so that its free end hangs 1.5 metres above ground. When block rests on the floor. The end A of the rope is moved horizontally in astraight line by a man walking at a uniform velocity V=3metres per second

Question

Find time taken by block to reach the pulley if h= 4.5metres that is from free end to centre of pulley

Answer 1

The man is walking away, so the horizontal distance the end of the rope has moved at time t is 3t meters.

Initially, there are 3 meters of rope from the free end to the pulley. So, at time t, the amount of rope from C to the man is

c^2 = 3^2 + (3t)^2= 9(1+t^2)

Now, the block must rise 4.5 meters, so we need

(4.5+3)^2 = 9(1+t^2)
2.5^2 = (1+t^2)
5.25 = t^2
t = 2.29 seconds