First slide

Projection Under uniform Acceleration

Question

Two projectiles are fired at different angles with the same magnitude of velocity, such that they have the same range. At what angles they might have been projected ?

Moderate

A

25^o and 65^o
B

35^o and 75^o
C

10^o and 50^o
D

None of these

Solution

We know that, $R = \frac{u^{2} \sin 2 θ}{g}$
Given that, $R_{1} = R_{2} and u_{1} = u_{2}$
$\begin{array}{l} ∴ R_{1} = \frac{{u_{1}}^{4} \sin 2 θ}{g} \\ and R_{2} = \frac{{u_{2}}^{2} \sin 2 (90^{\circ} - θ)}{g} \\ ∴ \sin 2 θ = \sin 2 (90^{\circ} - θ) = \cos 2 θ \end{array}$
Solving we get, $θ = 25^{\circ} .$ The other angle is $90^{\circ} - 25^{\circ} = 65^{\circ}$

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