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 an

Question

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 )

TestHub · Accepted Answer

For two projectiles with same speed to have the same horizontal range, angle of projection will be $θ_{1} + θ_{2} = 90 °$ .

Therefore, $θ_{2} = 90 ° - 60 ° = 30 °$ .

Now, required sum of maximum heights will be,

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

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

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