First slide

Rectilinear Motion

Question

If a body is projected vertically up, its velocity decrease to half of its initial velocity at a height ′h′ above the ground. Then maximum height reached by it is $\frac{p h}{3}$ . Find the value of $p$ .

Moderate

Solution

From A to B,
$v^{2} = u^{2} + 2 a s$
$\Rightarrow {(\frac{u}{2})}^{2} = {(u)}^{2} - 2 g h$
$\Rightarrow u^{2} = \frac{8 g h}{3}$ ……….(1)
From A to C,
$v^{2} = u^{2} + 2 a s$
$\Rightarrow 0 = {(u)}^{2} - 2 g H$
$\Rightarrow u^{2} = 2 g H$ ………..(2)

Equating (1) and (2)
$\frac{8 g h}{3} = 2 g H$
$\Rightarrow H = \frac{4 h}{3}$

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