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, v−h=2Vh or (v−h)2=4v2h or u2−2g−(−h)=4(u2−2gh) ∴u2=10gh3 Now, hmax=u22g=5h3