How Far Will the Ice Hockey Player Move When the Puck Reaches the Goal?

In this scenario, we are dealing with the conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event. Initially, both the ice hockey player and the puck are at rest, so the total momentum is zero.

When the ice hockey player hits the puck, the momentum of the player will be equal in magnitude but opposite in direction to that of the puck. Using the formula Momentum = mass x velocity, we can calculate the velocity of the player:

Velocity of player (v) = (mass of puck x velocity of puck) / mass of player

Plugging in the values, we get:

v = (0.157 kg x 44 m/s) / 82 kg = 0.08466 m/s

Next, to find the distance the player moves while the puck is traveling, we use the formula Distance = velocity x time. The time it takes the puck to reach the goal can be calculated by dividing the distance by the puck's velocity:

Time = Distance / Velocity of puck = 15.4 m / 44 m/s = 0.35 seconds

Therefore, the distance the player moves, d, is calculated as:

d = velocity of player x time = 0.08466 m/s x 0.35 s = 0.029632 m or 2.96 cm

In conclusion, the ice hockey player will move 2.96 cm in the time it takes the puck to reach the goal. This showcases the principles of physics and conservation of momentum in action.