Recent studies have raised concern about `heading\' inyouth soccer (i.e., hittin

Question

Recent studies have raised concern about `heading' inyouth soccer (i.e., hitting the ball with the head). A soccerplayer `heads' a size 5 ball deflecting it by 31.0°, and keepsits speed of 11.10 m/s constant. A size 5 ball has a mass ofapproximately 2.000 kg. What is the magnitude of the impulse whichthe player must impart to the ball?







If the player's head has a mass of 4.80 kg, whatis the magnitude of the average acceleration of the player's headduring the impact. Assume that over the brief time of the impact,27.80 ms, the player's head can be treated separately from theplayer's body.





If the player's head has a mass of 4.80 kg, whatis the magnitude of the average acceleration of the player's headduring the impact. Assume that over the brief time of the impact,27.80 ms, the player's head can be treated separately from theplayer's body.

Explanation / Answer

mass of 5 ball m = 2 kg initial velocity u = 11.1 m / s final velocity in initial direction v = 11.1 * cos 31 change in velocity in initial direction dv = u - v                                                           = 1.58544 impulse in initial direction = m * dv                                            = 3.17 kg m / s impulse in vertical to the initial direction = m* u sin 31                                                            = 11.43 kg m / s magnitude of impulse J = [ 3.17 ^ 2 + 11.43 ^ 2]                                    = 11.865 kg m / s force F = J / time             = 426.8 N So, required accleration a = F / 4.8 kg                                         = 88.91 m / s ^ 2

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