A stone thrown vertically upwards with a speed of $5 m / s$ attains a height $H_{1}$ . Another stone thrown upwards from the same point with a speed of $10 m / s$ attains a height $H_{2}$ . The correct relation between $H_{1}$ and $H_{2}$ is

H_{2} = 4 H_{1}

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H_{2} = 3 H_{1}

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H_{1} = 2 H_{2}

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H_{1} = H_{2}

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Solution

The correct option is B $H_{2} = 4 H_{1}$
From third equation of motion, $v^{2} = u^{2} + 2 a h$
In first case initial velocity $u_{1} = 5 m s^{- 1}$
final velocity $v_{1} = 0, a = g$
So, $0 = 25 - 2 g H_{1} \Rightarrow H_{1} = \frac{25}{2 g}$
and maximum height obtained is H1, then, $H_{1} = \frac{25}{2 g} . . . . . . . . . . . (1) 1$
In second case $u_{1} = 10 m s^{- 1}, v_{1} = 0, a = g$
So, $0 = 100 - 2 g H_{2} \Rightarrow H_{2} = \frac{100}{2 g}$
and maximum height obtained is H_2, then, $H_{2} = \frac{100}{2 g} . . . . . . . . . . . . . (2)$
from $(1)$ and $(2),$ we get,
$H_{2} = 4 H_{1}$

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