A soccer goalie (m = 65 kg) collides with the goalpost. If she was moving at 8 m/s and comes to rest in 1⁄2 a second, determine:

a) The impulse the post exerts on the player.
b) The impulse the goalie exerts on the post.
c) The average force exerted by the post.
d) The average force exerted by the goalie.

To solve this problem, we need to use the concept of impulse. Impulse is defined as the change in momentum of an object, and it can be calculated using the formula:

Impulse = Change in momentum = mass × change in velocity

Let's calculate the impulse for each scenario step by step.

a) To find the impulse the post exerts on the player, we first need to determine the change in velocity of the player. The initial velocity is given as 8 m/s, and the final velocity is 0 m/s (since the player comes to rest). Therefore, the change in velocity is:

Change in velocity = Final velocity - Initial velocity = 0 m/s - 8 m/s = -8 m/s

Now we can calculate the impulse:

Impulse = mass × change in velocity = 65 kg × (-8 m/s) = -520 kg·m/s

The negative sign indicates the direction of the impulse.

b) To find the impulse the goalie exerts on the post, we can use the fact that the total impulse in a system is zero (as per Newton's third law of motion). So, the impulse exerted by the goalie on the post will be equal in magnitude but opposite in direction to the impulse exerted by the post on the goalie. Therefore, the impulse exerted by the goalie on the post will also be 520 kg·m/s, but with a positive sign.

Impulse = 520 kg·m/s

c) To calculate the average force exerted by the post, we can use the concept of impulse and the fact that:

Impulse = Average force × Time

Since we have the impulse and the time (given as 1/2 second), we can rearrange the equation to solve for average force:

Average force = Impulse / Time = 520 kg·m/s / (1/2 s) = 1040 N

Therefore, the average force exerted by the post is 1040 Newtons.

d) Similarly, to calculate the average force exerted by the goalie, we can use the same formula:

Average force = Impulse / Time = 520 kg·m/s / (1/2 s) = 1040 N

So, the average force exerted by the goalie is also 1040 Newtons.

In summary:
a) The impulse the post exerts on the player is -520 kg·m/s.
b) The impulse the goalie exerts on the post is 520 kg·m/s.
c) The average force exerted by the post is 1040 Newtons.
d) The average force exerted by the goalie is 1040 Newtons.