A projectile is launched at a speed u and an angle heta above a horizontal field. If the coefficient of restitution for the impact between the projectile and the field is e , determine the distance from the launch point where the projectile experiences its second collision with the field.

Step-by-step solution

The horizontal range of the projectile before the first collision is R₁ = u^2 2 g . At the first collision, the horizontal component of velocity u remains unchanged, while the vertical component of velocity becomes e u directed upwards. The time of flight for the motion between the first and second collision is T₂ = 2(e u ) g . The horizontal distance covered between the first and second collision is R₂ = (u ) T₂ = 2 e u^2 g = e u^2 2 g . The total distance from the launch point to the second collision is R = R₁ +