First slide

Projectile motion

Question

If a stone is to hit at a point which is at a distance d away and at a height h (see figure) 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 $θ$ ?

Difficult

A

$\frac{g}{\cos θ} \sqrt{\frac{d}{2 (d \tan θ - h)}}$
B

$\frac{d}{\cos θ} \sqrt{\frac{g}{2 (d \tan θ - h)}}$
C

$\sqrt{\frac{g d^{2}}{h \cos^{2} θ}}$
D

$\sqrt{\frac{g d^{2}}{(d - h)}}$

Solution

$\begin{array}{l} h = (u \sin θ) t - \frac{1}{2} g t^{2} \\ d = (u \cos θ) t or t = \frac{d}{u \cos θ} \\ h = u \sin θ \frac{d}{u \cos θ} - \frac{1}{2} g \frac{d^{2}}{u^{2} \cos^{2} θ} \\ u = \frac{d}{\cos θ} \sqrt{\frac{g}{2 (d \tan θ - h)}} \end{array}$

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