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 51.0°, and keeps its speed of 17.30 m/s constant. A size 3 ball has a mass of approximately 2.000 kg.

If the player's head has a mass of 2.10 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, 36.20 ms, the player's head can be treated separately from the player's body.

Explanation / Answer

initial velocity = vix = 17.3 m/s

viy = 0

after hitting fina velocity vfx = 17.3*cos51 = 10.89 m/s

vfy = 17.3*sin51 = 13.44 m/s

change in momentum

dPx = m*(vfx-vix) = 2*(10.89-17.3)= -12.82 kg m/s

dPy = m*(vfy-viy) = 2*(13.44-0) = 26.88 kg m /s

impuse = cahnge in momentum

J = dPxi + dpyj

magnitude = J = sqrt(dpx^2+dpy^2)

lJl = 29.78 Ns   <----------answer

-----------------------------

but impulse is defined as the product of force and time of impact of force

J = F*t

F = J/t = 823 N

acceleration = F/m = 823/2.1 = 391.9 = 392 m/s^2 <-------answer

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