Question

The range of a projectile when launched at an angle $θ$ is same as when launched at an angle 2 $θ$ . What is
the value of $θ$ ?

Moderate

Solution

Range of projectile launched at an angle $θ$ is same as the range of projectile launched at angle 2 $θ$ .
$\Rightarrow \frac{u^{2} \sin 2 (2 θ)}{g} = \frac{u^{2} \sin 2 θ}{g}$
$\Rightarrow$ sin2(2 $θ$ ) = sin2 $θ$
$\Rightarrow$ 2 sin 2 $θ$ cos 2 $θ$ = 2 sin $θ$ cos $θ$
4 sin $θ$ cos $θ$ cos 28 = 2 sin $θ$ cos $θ$
$\Rightarrow 4 \cos 2 θ = 2 \Rightarrow \cos 2 θ = \frac{1}{2}$
$\Rightarrow$ cos 2 $θ$ = cos 60⁰
$\Rightarrow$ 2 $θ$ = 60⁰
$∴$ $θ$ = 30⁰

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