Two bodies are projected from ground with same speeds 40 m at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60° with horizontal then sum of the maximum heights,

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Solution

Q.
Two bodies are projected from ground with same speeds 40 m $s^{- 1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60° with horizontal then sum of the maximum heights, attained by the two projectiles, is ______ m. (Given g = 10 m $s^{- 2}$ ) [2023]

Ans.
(80)

Since range is same

$\Rightarrow θ_{1} + θ_{2} = 90 °$

$\Rightarrow θ_{2} = 30 °$

$\Rightarrow {(H_{\max})}_{1} + {(H_{\max})}_{2}$ $= \frac{U^{2} \sin^{2} θ_{1}}{2 g} + \frac{U^{2} \sin^{2} θ_{2}}{2 g}$

$= \frac{40^{2}}{20} (\frac{1}{4} + \frac{3}{4}) = 80 m$

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