A 2 kg mass is dropped from rest in vacuum for 2 s. What is its momentum after 2 s? (take g = 9.8 m/s^2, downward)

A 2 kg mass is dropped from rest in vacuum for 2 s. What is its momentum after 2 s? (take g = 9.8 m/s^2, downward)

• A. 19.6 kg·m/s
• B. 39.2 kg·m/s downward
• C. 39.2 kg·m/s upward
• D. 19.6 kg·m/s upward

Answer: (B)

Momentum equals mass times velocity. Since it’s dropped from rest in vacuum, gravity provides the only acceleration, so after 2 seconds the velocity is v = g t = 9.8 m/s^2 × 2 s = 19.6 m/s downward. The momentum is p = m v = 2 kg × 19.6 m/s = 39.2 kg·m/s, directed downward. So the momentum after 2 seconds is 39.2 kg·m/s downward.

Momentum equals mass times velocity. Since it’s dropped from rest in vacuum, gravity provides the only acceleration, so after 2 seconds the velocity is v = g t = 9.8 m/s^2 × 2 s = 19.6 m/s downward. The momentum is p = m v = 2 kg × 19.6 m/s = 39.2 kg·m/s, directed downward. So the momentum after 2 seconds is 39.2 kg·m/s downward.