Question

A projectile is fired at an angle $\theta$ with the horizontal. The condition under which it lands perpendicular on the fixed inclined plane with inclination α as shown in figure is,

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

To strike the plane perpendicularly, Final velocity along the plane is zero.

Along the inclined plane, we have,

i.e u cos ($\theta$ - $\alpha$) = g sin $\alpha$t $\Rightarrow$ (1)

Also, the range of the projectile over the inclined plane is,

t = $\frac{2usin(\theta -\alpha )}{gcos\alpha }$$\Rightarrow$ (2)

$\therefore$ u cot ($\theta$ - $\alpha$) = 2 tan $\alpha$ $\times$ u

$\therefore$cot ($\theta$ - $\alpha$) = 2 tan $\alpha$