Question

An ice hockey forward with mass 75.0 kg is skating due north with a speed of 5.50 m/s. As the forward approaches the net for a slap shot, a defensive player (mass 110 kg) skates toward him in order to apply a body-check. The defensive player is traveling south at 4.40 m/s just before they collide.

If the two players become intertwined and move together after they collide, in what direction and at what speed do they move after the collision? Friction between the two players and the ice can be neglected.

Express your answer with the appropriate units. Enter positive value if the velocity is northward and negative value if the velocity is southward.

Answer 1

After the collision, the two players, one a hockey forward with a mass of 75.0 kg and the other a defensive player with a mass of 110 kg, will move southward at a speed of approximately 0.387 m/s, as determined by conservation of momentum.

Step-by-step explanation:

To determine the direction and speed at which both the hockey forward and the defensive player move after they become entangled and move together after the collision, we use the principle of conservation of momentum. In an isolated system (ignoring external forces like friction), the total momentum before the collision equals the total momentum after the collision.

The momentum of the hockey forward before the collision can be calculated using the formula p = mv, where m is the mass and v is the velocity. Therefore, the forward's momentum is 75.0 kg × 5.50 m/s = 412.5 kg·m/s northward.

Similarly, the defensive player's momentum is 110 kg × 4.40 m/s (but southward) = 484 kg·m/s southward. Because the defensive player is moving south, we take this momentum as negative when we sum up the momentum.

To find the post-collision velocity, we use the formula ((m1 × v1) + (m2 × v2)) / (m1 + m2), where m1 and m2 are the masses of the two players and v1 and v2 are their velocities. Plugging in the numbers we get:

((75.0 kg × 5.50 m/s) + (110 kg × -4.40 m/s)) / (75.0 kg + 110 kg) = (412.5 kg·m/s - 484 kg·m/s) / 185.0 kg = -71.5 kg·m/s / 185.0 kg

The result is approximately -0.387 m/s, which indicates they would move southward since the velocity is negative.