Recent studies have raised concern about `heading\' in youth soccer (i.e., hitti

Question

Recent studies have raised concern about `heading' in youth soccer (i.e., hitting the ball with the head). A soccer player `heads' a size 4 ball, deflecting it by 54.0°, but keeping its speed of 16.80 m/s constant. A size 4 ball has a mass of approximately 0.296 kg.

a) What is the magnitude of the impulse which the player imparts to the ball?

b) If the player's head has a mass of 4.00 kg, what is the magnitude of the average acceleration of the player's head during the impact? Assume that over the brief time of the impact, 24.30 ms, the player's head can be treated separately from the player's body.

Explanation / Answer

a) (delta v)2 = 16.82 + 16.82 - (2 * 16.8 * 16.8 * cos 54)

= 15.25 m/s

magnitude of impulse = m * delta v

= 0.296 * 15.25

impulse = 4.515 kg.m/s

b) F = I / t = 4.515 / 0.0243 = 185.8 N

a = F / m = 185.8 / 4.00

magnitude of average acceleration = 46.45 m/s2

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