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 3 ball deflecting it by 34.0°, and keeps its speed of 12.80 m/s constant. A size 3 ball has a mass of approximately 2.000 kg. What is the magnitude of the impulse which the player must impart to the ball?


b. If the player's head has a mass of 2.40 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, 37.60 ms, the player's head can be treated separately from the player's body.

Explanation / Answer

a) We know that the impulse imparted by the player could be determined by the change in momentum of the ball.

Impulse = F.dt = dP = Pf - Pi

Here F = force , dt = short interval of time, dP = Change in momentum , Pf = Final momentum , Pi = initial momentum

Let the initial momentum pi = o kg m/s

Final momentum = Pf = ?

There will be two components of final momentum. Pf y = Psin 34 = mVsin 34

Pfy = 2(12.8) sin 34 = 10.41 Kg m/s

Pf x = 2(12.8) cos 34 = 21.22 Kg m/s

Magnitude of total momentum

Pf =( Pfx2 + Pfy2)1/2

=( 21.22 + 10.412 )1/2

= 23.63 Kg m/s

Now putting in the equation of impulse

Impulse = Pf - Pi

= 23.63 - 0

= 23.63 Kg m/s

b) BY the formula of Impulse

Impulse = F.dt

Impulse = ma dt

a = Impulse / m dt

a = 23.63(1000) / 2.40 (37.6)

a = 261.9 m /s2

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