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Q.

Two bodies are projected from ground with same speeds 40 ms^-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 height, attained by the two projectile, is ____m. (Given g =10 ms^-2)

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Detailed Solution

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Range of a projectile motion is given by

$R = \frac{u^{2} \sin 2 θ}{g}$

and Maximum height by

$H = \frac{u^{2} \sin^{2} θ}{2 g}$

$∵$ Ranges are same for angles of projection $θ_{1} = 60^{0} & θ_{2} = 30^{0}$
$H_{1} + H_{2} = \frac{u^{2} \sin^{2} 60}{2 g} + \frac{u^{2} \sin^{2} 30}{2 g} \begin{array}{l} = \frac{u^{2}}{2 g} [\frac{3}{4} + \frac{1}{4}] \\ = \frac{u^{2}}{2 g} = \frac{40 \times 40}{2 \times 10} = 80 m \end{array}$

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