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Question

# The figure shows two positions A and B at the same height h above the ground. If the maximum height of the projectile is H, then determine the time t elapsed between the positions A and B in terms of H.

A

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B

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C

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D

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Solution

## The correct option is C Time of flight for this part of motion (between points A and B, both at height h) assuming speed of projection to be v and angle of projection to be α T = 2v sinαg ---------(I) Now we have to eliminate v & α as these variables we assumed. Hmmmmm..........How do we do that, okay what else is given? Yes, the maximum height i.e. (H−h). ⇒ (H−h) = v2 sin2α2g ----------(II) Thank goodness! Now from equation (I) ⇒ v sin α = Tg2 Equation (II) ⇒ (H−h) = T2g24(2g) ⇒(H−h) = gT28 ⇒ T = √8(H−h)g

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