First slide

Projection Under uniform Acceleration

Question

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 $θ$ ?

Moderate

A

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

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

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

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

Solution

$h = (u \sin θ) t - \frac{1}{2} {gt}^{2}$
$d = (u \cos θ) t$
or $t = \frac{d}{u \cos θ}$
h = u sin $θ$ $. \frac{d}{u \cos θ} - \frac{1}{2} g \frac{d^{2}}{u^{2} \cos^{2} θ}$
$u = \frac{d}{\cos θ} \sqrt{\frac{g}{2 (d \tan θ - h)}}$

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