Question

From the foot of an inclined plane of inclination $\alpha$, a projectile is shot at an angle $\beta$ with the inclined plane. Find the relation between $\alpha$ and $\beta$ if the projectile strikes horizontally.

• A. $\frac{2\sin \beta }{\cos \alpha }=\sin (\alpha +\beta )$
• B. $\frac{\sin \beta }{\cos \alpha }=\sin (\alpha +\beta )$
• C. $\frac{3\sin \beta }{\cos \alpha }=\sin (\alpha +\beta )$
• D. $\frac{\sin \beta }{\cos \alpha }=2\sin (\alpha +\beta )$

Answer 1

The correct option is A $\frac{2\sin \beta }{\cos \alpha }=\sin (\alpha +\beta )$

Projectile with respect to ground

$\theta =\alpha +\beta$

time when velocity is horizontal: $t=\frac{usin(\alpha +\beta )}{g}$

Projectile with respect to incline plane $\theta =\beta \dots \left(1\right)$

time when it strikes surface is: $t=\frac{2u_y}{a_y}$

where$u_y=usin\beta ,a_y=gcos\alpha$

$t=\frac{2usin\beta }{gcos\alpha }\dots \left(2\right)$

from $\left(1\right)\&\left(2\right)$

$\frac{2sin\beta }{cos\alpha }=sin(\alpha +\beta )$