BotanyA body is projected from point A on an inclined plane having inclination θ with horizontal with velocity u in a direction perpendicular to the inclined plane as shown in figure. Then range of the projectile on inclined plane is

A body is projected from point A on an inclined plane having inclination θ with horizontal with velocity u in a direction perpendicular to the inclined plane as shown in figure. Then range of the projectile on inclined plane is

A
$\frac{2 u^{2}}{g} tanθ . secθ$
B
$\frac{u^{2}}{g} \sin 2 θ . cosθ$
C
$\frac{2 u^{2}}{g} secθ$
D
$\frac{u^{2}}{g} sinθ$

Solution:

Considering X axis along inclined plane and Y axis perpendicular to inclined plane.

$\begin{array}{l} T_{i} = Time of flight on inclined plane \\ = \frac{2 u}{gcosθ} \\ ∴ R_{i} = \frac{1}{2} (gsinθ) {T_{i}}^{2} = \frac{1}{2} (gsinθ) (\frac{4 u^{2}}{g^{2} \cos^{2} θ}) \\ R_{i} = \frac{2 u^{2}}{g} tanθ . secθ \end{array}$