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 5 ball, deflecting it by 45.0°, but keeping its speed of 17.40 m/s constant. A size 5 ball has a mass of approximately 0.401 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 4.70 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, 26.20 ms, the player's head can be treated separately from the player's body.

Explanation / Answer

here,

theta = 45 degree

initial speed , u = 17.4 m/s

a)

the magnitude of the impulse which the player imparts to the ball, P = mass of ball * u

P = 0.401 * 17.4 kg.m/s = 6.98 kg.m/s

b)

time taken , t = 26.2 ms = 0.0262 s

the magnitude of the average acceleration of the player's head during the impact , a = P/(t * mass of head)

a = 6.98 /( 0.0262 * 4.7) m/s^2

a = 56.7 m/s^2

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