If a stone is to hit at a point which is at a distance $d$ away and at a height $h$ above the point from where the stone starts, then what is the value of initial speed $u$ , if the stone is launched at an angle $θ ?$

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TestHub · Accepted Answer

Using equation of motion for projectile in x and y-direction.

$h = (u sin θ) t - \frac{1}{2} g t^{2}$

$d = (u cos θ) t$ or $t = \frac{d}{u cos θ}$

$⟹ h = u sin θ . \frac{d}{u cos θ} - \frac{1}{2} g . \frac{d^{2}}{u^{2} {cos}^{2} θ}$

$⟹ u = \frac{d}{cos θ} \sqrt{\frac{g}{2 (d t an θ - h)}}$

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