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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 ?

2 years ago

Answers : (1)

Arun
24742 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

2 years ago
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