A 84.0 kg ice hockey player hits a 0.150 kg puck, giving the puck a velocity of 36.0 m/s. If both are initially at rest and if the ice is frictionless, how far (in m) does the player recoil in the time it takes the puck to reach the goal 24.0 m away? (Enter the magnitude.)

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Explanation:Set term u equal to initial velocity for simplicity

Set V equal to final velocity for simplicity

2

To begin this problem, one must look at the system to have multiple stages. These being before and after hitting the puck. In these first few steps, we look at BEFORE the human hits the puck

3

This collision is elastic because the puck and the human do not join together after interaction

4

Because the initial velocity of both the puck and the human are both 0, the terms on the left of the equal sign become 0

5

Solving for the final velocity of the human gives this formula. This number should be negative as the negative indicates the direction he is going (left)

The final velocity of the puck is already given in the problem

6

Because the ice is frictionless, the final velocity before hitting the puck is equal to the initial velocity after hitting the puck

Now we begin to look at the system AFTER the puck has been hit

7

Using the formula for final position allows us to solve for time it takes the puck to travel the distance given

8

9

Solve for time

10

We can now use the formula for the final position of the human to solve for the final answer

11

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Plugging in formulas from steps 5 and 9 gives the final answer

total distance/total time

(85 + 82)/(5+3)

167/8

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