Question

A. 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 40.0°, and keeps its speed of 13.20 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 2.90 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, 30.40 ms, the player's head can be treated separately from the player's body.

Answer 1

a. The magnitude of the impulse which the player must impart to the ball is 17.25 kg.m/s.

b. The magnitude of average acceleration of the player's head during the impact is   195.66 m/s².

What is impulse?

The change in momentum is equal to the product of impact force applied while colliding and time for that impact.

Impulse F. t = m (Vf -Vi)

where, Vf is the final velocity and Vi is the initial velocity.

Given, a soccer player 'heads' a size 3 ball deflecting it by 40.0°, and keeps its speed of 13.20 m/s constant. A size 3 ball has a mass of approximately 2.000 kg.

a. Substitute the values into the expression, we get

Impulse (x) = 2 x (13.20 - 13.20cos40°)

Impulse  (x) = 3.088 kg.m/s

Impulse in y direction, is

Impulse (y) = 2 x  13.20sin40°

Impulse (y)  = 16.97 kg.m/s

so, the magnitude of impulse is

I = sq rt(Ix² + Iy²)

Put the values, we get

I = 17.25 kg.m/s

Thus, the magnitude of the impulse which the player must impart to the ball is 17.25 kg.m/s

b. The player's head has a mass of 2.90 kg. The brief time of the impact, 30.40 ms,

F.t = I

Put the given values, we have

F = 17.25 / 30.40 x 10⁻³

F = 567.434 N

From the Newtons second law of motion,

F = ma

Plug the values from the question, we have

567.434 N =  2.90 x a

a = 195.66 m/s²

Thus the magnitude of average acceleration of the player's head during the impact is  195.66 m/s².

Learn more about impulse.

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