Confused about force/impulse/acceleration

[lmlgrey]

The question goes

1. Recent studies have raised concern about `heading' in youth soccer (i.e., hitting the ball with the head). A soccer player `heads' a size 5 ball, deflecting it by 58.0 deg, but keeping its speed of 15.80 m/s constant. A size 5 ball has a mass of approximately 0.426 kg. What is the magnitude of the impulse which the player imparts to the ball? and If the player's head has a mass of 4.70 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, 21.00 ms, the player's head can be treated separately from the player's body.



I solved the first question by calculating the change in velocity of the ball and that multiplies the mass gives me the impulse. It turns out right. HOWEVER, when i tried to do the second part, what did first was to use the conservation of momentum:
m1v1+m2v2=m1vf1+m2vf2
whereas m1 is the head, and m2 is the ball
to get that

change in velocity in v1(the head)= m2(v2-vf2)/m1

since acceleration = change in velocity / times
then its pretty obvious to say that acceleration is solved by the above formula.

but the computer says the answer is wrong. Then i attemped to divide the impulse which i got from the first question by time, and i got the net force, dividing the force again gives me the CORRECT acceleration.

Can someone explain to me why the my first attempt to the 2nd question didnt work?

thanks!

 

[alphysicist]

Hi lmlgrey,

The question goes

1. Recent studies have raised concern about `heading' in youth soccer (i.e., hitting the ball with the head). A soccer player `heads' a size 5 ball, deflecting it by 58.0 deg, but keeping its speed of 15.80 m/s constant. A size 5 ball has a mass of approximately 0.426 kg. What is the magnitude of the impulse which the player imparts to the ball? and If the player's head has a mass of 4.70 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, 21.00 ms, the player's head can be treated separately from the player's body.



I solved the first question by calculating the change in velocity of the ball and that multiplies the mass gives me the impulse. It turns out right. HOWEVER, when i tried to do the second part, what did first was to use the conservation of momentum:
m1v1+m2v2=m1vf1+m2vf2
whereas m1 is the head, and m2 is the ball
to get that

change in velocity in v1(the head)= m2(v2-vf2)/m1

What numbers did you use for the velocities here? and what did you get for the velocity and acceleration of the head?