A projectile is launched from the origin with velocity components ux = 10 m/s and uy = 20 m/s. A smooth vertical wall is located at x = 10 m. The coefficient of restitution between projectile and wall is e = 1/2. Take g = 10 m/s². If the projectile finally lands at x = −N m, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
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Question

A projectile is launched from the origin with velocity components ux = 10 m/s and uy = 20 m/s. A smooth vertical wall is located at x = 10 m. The coefficient of restitution between projectile and wall is e = 1/2. Take g = 10 m/s². If the projectile finally lands at x = −N m, find N.

Physics · Center of maas , Momentum and Collision · collision and types of collision

G1 Physics · Accepted Answer

Time to reach the wall: t1 = 10/10 = 1 s. Height at the wall: y1 = uy t1 − (1/2)gt1² = 20(1) − 5(1)² = 15 m. Vertical velocity at impact: vy1 = uy − gt1 = 20 − 10 = 10 m/s upward. The wall is smooth, so vy is unchanged during collision. The horizontal velocity reverses and becomes vx(after) = −e ux = −5 m/s. Let τ be the time from wall collision until the projectile reaches the floor. Vertical motion: 0 = 15 + 10τ − 5τ². Divide by 5: 0 = 3 + 2τ − τ² ⇒ τ² − 2τ − 3 = 0 ⇒ τ = 3 s (positive root).…