A Frictionless Collision Problem: The Final Speed of a Rock After Being Hit by a Hockey Puck
A hockey puck with mass M travels across a frictionless icy pond with an initial velocity of 3.0[ m/s]. It collides with a stationary rock that has mass 4M. The hockey puck bounces off of the rock, and leaves with a speed of 2[ m/s] in the exact opposite direction it was originally traveling. What is the approximate final speed of the rock?
Final answer:
Using the conservation of momentum, the final speed of the rock after a frictionless collision with a hockey puck is calculated to be approximately 1.25 m/s.
Explanation:
The final speed of the rock after being hit by a hockey puck can be determined using the conservation of momentum, which states that the total momentum of a system before collision is equal to the total momentum after collision when external forces are negligible (which they are in a frictionless environment). We are given that the initial velocity of the hockey puck is 3.0 m/s, the mass of the puck is M, and the mass of the rock is 4M. The puck bounces back with a speed of 2 m/s in the opposite direction.
Using the conservation of momentum:
- Initial total momentum = Momentum of puck + Momentum of rock
- (M)(3.0 m/s) + (4M)(0 m/s) = (M)(-2.0 m/s) + (4M)(v), where v is the final velocity of the rock
- 3.0M = -2.0M + 4Mv
- 4Mv = 5M
- v = 5M / 4M
- v = 1.25 m/s
The final speed of the rock is therefore approximately 1.25 m/s.