A 0.45 kg soccer ball approaches a player horizontally with a velocity of magnitude equal to 35 m/s. The player heads the ball straight back out horizontally, and the magnitude of the ball’s velocity after the collision is 40 m/s. The contact time between their head and the ball is 5 ms. What average force does his head experience?

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To find the average force experienced by the player's head, we can use the impulse-momentum principle. According to this principle, the change in momentum of an object is equal to the impulse applied to it. The impulse can be calculated by multiplying the average force by the contact time.

The change in momentum of the soccer ball can be calculated as:

Δp = m * (vf - vi)

Where:
Δp = change in momentum
m = mass of the soccer ball
vf = final velocity of the soccer ball
vi = initial velocity of the soccer ball

In this case, the initial velocity of the soccer ball is 35 m/s, final velocity is -40 m/s (since it's heading back), and the mass is 0.45 kg.

Using the formula, we can calculate the change in momentum:

Δp = 0.45 kg * (-40 m/s - 35 m/s)

Next, we can find the impulse by multiplying the change in momentum by the contact time:

Impulse = Δp * Δt

Where:
Impulse = m * (vf - vi) * Δt

In this case, the contact time is given as 5 ms, which needs to be converted to seconds before we can use it in the equation:

Δt = 5 ms = 5 * 10^(-3) s

Now, we can find the impulse:

Impulse = (0.45 kg * (-40 m/s - 35 m/s)) * (5 * 10^(-3) s)

Finally, we know that impulse is equal to the average force multiplied by the contact time, so we can rearrange the equation to solve for the average force:

Average Force = Impulse / Δt

Putting it all together:

Average Force = [(0.45 kg * (-40 m/s - 35 m/s)) * (5 * 10^(-3) s)] / (5 * 10^(-3) s)

Now, we can calculate the average force.