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Question

A body falling freely from a given height H, hits an inclined plane in its path at a height h. As a result of this impact the direction of velocity of the body becomes horizontal. For what value of hH will the body take maximum time to reach the ground?

A
12
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B
14
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C
1
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D
34
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Solution

The correct option is A 12
Let say from the point O to B time taken is t1
Hh=12gt12 t1=2(Hh)g
from the point B to C time taken is t2.
h=12gt22 t2=2hg
Total time T=t1+t2=2g((Hh)1/2+h12]

For T to be maximum

dTdh=0
12(Hh)(12)(1)+12h(12)= 0Hh= h hH=12

For detailed solution watch the next video.


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