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Question

From an elevated point A, a stone is projected vertically upwards. When the stone reaches a distance h below A, its velocity is double of what it was at a height h above A. Show that the greatest height attained by the stone is 53h.

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Solution

Let u be the velocity with which the stone is projected vertically upwards. Given that, vh=2Vh
or (vh)2=4v2h
or u22g(h)=4(u22gh)
u2=10gh3
Now, hmax=u22g=5h3

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