Question

Which of the following statements are true regarding a projectile projected from the bottom of the inclined plane ?

• A. The direction of projection to get maximum range divides the angle between the vertical and the inclined plane in the ratio of $1:2$.
• B. The direction of projection to get maximum range divides the angle between the vertical and the inclined plane in the ratio of $2:1$.
• C. The direction of projection to get maximum range divides the angle between the vertical and the inclined plane in the ratio of $1:1$.
• D. The direction of projection to get maximum range divides the angle between the vertical and the inclined plane in the ratio of $3:1$.

Answer 1

The correct option is C The direction of projection to get maximum range divides the angle between the vertical and the inclined plane in the ratio of $1:1$.

Condition for maximum range in case of projectile motion on an inclined plane from the bottom is given by
$2\alpha -\theta =\frac{\pi }{2}or\alpha -\theta =\frac{\pi }{2}-\alpha$ (i)

From the figure, we can say that the angle made by the direction of projection with the inclined plane is $\alpha -\theta$
Angle made by the vertical component with direction of projection is $\frac{\pi }{2}-\alpha$

Thus, using equation(i), we can say that the angle made by the direction of projection with the inclined plane and with the vertical are equal.

Thus, the direction of projection divides the angle between the vertical and the inclined plane in the ratio of $1:1$.