A projectile projected at an angle q with the horizontal and velocity u has a horizontal velocity u cos q and vertical velocity u sin q. During collision with the ground only the vertical component undergoes a change because, it is perpendicular to the surface at which it is colliding. The horizontal component does not undergo any change because it is parallel to the surface.
The vertical component becomes e usin q after the first collision and e2 usin q after the second collision and so on. Therefore after nth collision the vertical component becomes
V1 = en u sin q -------------(1)
And the horizontal component remains
V2 = u cos q --------------(2)
Therefore the magnitude of the velocity after nth collision will be
Vn = Ö V12 + V22 ---------------- (3)
And its direction of motion with the horizontal will be
a = Tan -1 ( V1 / V2) ------------------ (4)
Moderation Team
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