First slide

Projection Under uniform Acceleration

Question

A ball is projected horizontally with a speed v from the top of plane inclined at an angle $45^{0}$ with the horizontal. How far from the point of projection will the ball strike the plane?

Moderate

A

$\frac{2 v^{2}}{g}$
B

$\sqrt{2} [\frac{2 v^{2}}{g}]$
C

$\frac{v^{2}}{g}$
D

$\sqrt{2} \frac{v^{2}}{g}$

Solution

x = vt or y = $\frac{1}{2} {gt}^{2}$
${tan 45}^{0} = \frac{y}{x}$
or y = x
or $y = \frac{{gx}^{2}}{2 v^{2}} or x = \frac{{gx}^{2}}{2 v^{2}} or x = \frac{2 v^{2}}{g}$
Also, $y = \frac{2 v^{2}}{g} or l^{2} = x^{2} + y^{2}$
l = $\sqrt{2} \times x$
or l = $\sqrt{2} [\frac{2 v^{2}}{g}]$

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