A projectile is fired at an angle ? on an inclined plane with angle a find the condition for which it lands perpendicularly on incline.When does the projectile land perpendicularly? Shouldnt it land with angle ? only??

let b be the angle of projection with the inclined plane whose inclination is a

then the condition for it to land perpendicular the plane is 2tan(b-a)=cota

if the projectile land on the surface horizontally(parallel to ground ) then tanb = cota+2tana

it can be easily derived from the formulas of motion on inthe inclined plane such as

x=ucos(b-a)t -(1/2)gsin(a)t^2

y= usin(b-a)t-(1/2)gcos(a)t^2

by appling the condition.

Approved