A 0.110-kg hockey puck, moving at 35.0 m/s, strikes a 0.290-kg jacket that is thrown onto the ice by a fan of a certain hockey team. The puck and jacket slide off together. Find their velocity. (Take the positive direction to be that of the initial direction of the puck.)
The initial momentum of the puck and the final momentum of the puck and jacket, moving together, are the same.
Write that in equation form and solve for the final velocity.
To find the velocity of the puck and jacket after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity (p = m*v).
Before the collision, the momentum of the puck is given by the equation:
Momentum_puck_initial = mass_puck * velocity_puck_initial
After the collision, the momentum of the combined system (puck and jacket) is given by the equation:
Momentum_combined = (mass_puck + mass_jacket) * velocity_combined
Since the total momentum before and after the collision is the same, we can set up the equation:
mass_puck * velocity_puck_initial = (mass_puck + mass_jacket) * velocity_combined
Now let's substitute the given values into the equation:
mass_puck = 0.110 kg
velocity_puck_initial = 35.0 m/s
mass_jacket = 0.290 kg
0.110 kg * 35.0 m/s = (0.110 kg + 0.290 kg) * velocity_combined
Now solve for velocity_combined:
0.110 kg * 35.0 m/s = (0.110 kg + 0.290 kg) * velocity_combined
3.85 kg·m/s = 0.400 kg * velocity_combined
velocity_combined = 3.85 kg·m/s / 0.400 kg
velocity_combined ≈ 9.63 m/s
Therefore, the velocity of the puck and jacket together after the collision is approximately 9.63 m/s in the positive direction.