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