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Grade: 11


A stone is dropped from a height h, simultaneously another stone is thrown up from the ground which attains a maximum height 4h, the two stones cross each other at time ?

3 years ago

Answers : (1)

25768 Points

For upper stone which is dropped downwards the distance traveled is


S1 = ut + 1/2  g t^2


Here u = 0


g = accln due to gravity = 9.8 m/s2


So S1 = 1/2g t2


Distance of stone from ground is = h - S1 = h -  0.5 g t2    ....(1)


Now for stone thrown upwards such that it goes to height 4h from ground


Potential energy at top = Kinetic energy from the point of projection


or mg(4h) = 1/2 m u2


or u = (8hg)1/2


Thus S2 = ut  -  0.5 g t2


or S=  (8hg)1/2 t - 0.5 g t2   ........(2)


Now for the two stones to meet


h - S1 = S2  


or h -  0.5 g t2   =  (8hg)1/2 t - 0.5 g t2                (from 1 and 2)


or h = (8hg)1/2 t 


or t = ( h/8g) 1/2

3 years ago
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