On June 20, 2013 Abby Wambach of the US Women\'s National Team scored 4 goals to

Question

On June 20, 2013 Abby Wambach of the US Women's National Team scored 4 goals to break the world record for international goals scored. A significant percentage of her goals are scored by using her forehead to redirect the ball into the goal. The mass of the soccer ball used is 450. g. If the initial velocity of the ball is v_l = -83.7i +37.0/ km/hr and the final velocity after collision is v_f = 90.0i km/hr. What is the impulse delivered to the ball by collision with her forehead? Assume momentum is conserved in this collision. If the mass of her head is 4.50 kg, what is the velocity with which her head recoils after the collision? Assume her head has an initial velocity v_l = 12.0i km/hr.

Explanation / Answer

m =450g

vi = -83.7 i+37 j km/hr

vf =90i km/hr

(a) Impulse =change in momentum = mvf -mvi

= 0.45(90i +83.7i -37j) = (78.165i - 16.65)kg.km/hr

Impulse =(21.7125i -4.625j) kg.m/s

b) From conservation of momentum

m1v1i+m2v2i =m1v1f+m2v2f

m1(v1i-v1f)+m2v2i =m2v2f

4.5*v2f = -(21.7125i -4.625j) +(4.5*12i)

4.5*v2f = 32.2875 i +4.625j

Velocity of head after collision v2f = (7.175 i+1.028 j) km/hr

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