From the top of a cliff 30m high,a stone is dropped.At that time,another stone is projected upward from 'a' the ground with a speed of 30m/s.After how much time and what height from the ground will the two stones cross each other?

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Answer 1 · 2018-06-06T17:36:56

The time is #=1s# and the height is #=25.1m#

Let the time, when the crossing takes place, be #=ts#

Apply the equation of motion

#s=ut+1/2g t^2#

The initial velocity is #=ms^-1#

The acceleration due to gravity is #g=9.8ms^-2#

For the stone dropped from the top, the equation is

#s=0*t+1/2g t^2=1/2*9.8*t^2=4.9t^2#

For the stone projected from the ground,

#30-s=30t-1/2g t ^2= 30t-4.9t^2#

Therefore,

#30-4.9t^2=30t-4.9t^2#

#30t=30#

#t=1s#

The height is

#s=4.9*1^2=4.9m# from the top

The height is #=30-4.9=25.1m # from the ground