A kid at the junior high cafeteria wants to propel an empty milk carton along a lunch table by hitting it with a 3.0g spit ball.

If he wants the speed of the 40g carton just after the spit ball hits it to be 0.30 m/s, at what speed should his 3.0 g spit ball hit the carton?

4.3 m/s

Explanation:

Using conservation of momentum, assume that the collision is elastic and that the 3.0 g ball stuck with the carton

3.0 g = 3 / 1000 = 0.003 kg = m₁

40 g = 40 / 1000 = 0.04 kg = m₂, u₂ = 0 since the body is stationary and v = 0.3m/s

m₁u₁ + m₂u₂ = v (m₁ + m₂)

0.003 u₁ = 0.30 (0.003 + 0.04) = 0.0129

u₁ = 0.0129 / 0.003 = 4.3 m/s