What is the Correct Calculation for Impulse in Soccer Heading?

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Recent discussions highlight the complexities of calculating impulse in soccer heading, particularly for youth players. To determine the impulse, one must first calculate the change in momentum by finding the initial and final momentum vectors. The initial momentum is derived by multiplying the initial speed by the ball's mass, while the final momentum requires calculating the new speed components after the ball is deflected. The correct impulse is then found by subtracting the initial momentum vector from the final momentum vector. This approach clarifies the distinction between impulse and momentum, emphasizing the importance of direction in the calculations.
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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 54.0°, and keeps its speed of 10.30 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?
I started by finding the change in velocity.
In the x-direction:
the final velocity= cos 54 * 10.30 * 2.000 = 12.1 m/s
the inital velocity = 10.30 * 2.000 = 8.3 m/s
Change in velocity in x= 3.8 m/s
In the y-direction:
the final velocity= sin 54 * 10.30 * 2.000= 16.6
the initial velocity= 0 m/s
change in velocity in y= 16.6 m/s
Then i used the pythagorean theorem.
sq rt 16.6^2 + 3.8^2 = 17.0 m/s
I multiplied this by the mass 2.000 to get the impulse= 34.0 kg*m/s
This wasn't right.. can someone tell me what I'm doing wrong?thanks
 
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The impulse is the change in momentum. So first you have to find the new speed vector (the new x and y speeds, multiply (the sqrt of them squared as you did) by mass to get the momentum vector (then get the new x and y momentum components with trig), and then subtract the initial momentum vector from the knew one (x-axis minus x-axis and y=axis minus y-axis), then find the size of the new vector to get the impulse.
-Also, when you calculated the velocities, why did you multiply by 2.000?
you found the new momentum, not the impulse.
 
I'm sorry but I really don't follow you. I think you're saying what I did was right but it's momentum not impulse. I'm not sure how to get the initial momentum.
 
The speed doesn't change, just the direction. Find the change in momentum by subtracting the initial momentum vector from the final momentum vector. Then find the magnitude of that change, which is all you need. (Hint: Pretend the initial momentum is in the +x direction.)
 
You get the initial momentum by simply multiplying the speed by the mass, as Doc AI said, all of the initial speed is along the x-axis.
 
I see what I was doing wrong. Thanks
 
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