A projectile is projected horizontally with velocity from the top of an inclined plane of inclination θ. How far from the point of projection will the projectile hit tht plane?
Consider a projectile, which is projected with velocity 'u' in horizontal direction from a point O on an inclined plane and hit the inclined plane at P↔(x, y).
Let O be the origin.
The horizontal direction is positive direction of X-axis and vertically downward direction is positive direction of Y-axis.
On resolving the components of velocity and acceleration in horizontal and vertical direction, we have
Motion along horizontal direction is,
Motion along vertical direction is,
Eliminating 't' from (1) and (2),
The equation of inclined plane is,
The point P is the intersection of trajectory and inclined plane, thus the coordinates of P are the solutions of equation (3) and (4).
By solving (3) and (4), we obtain
Therefore distance OP is,
So, the distance travelled by the projectile is OP.