Calculating the magnitude of an impulse

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    Impulse Magnitude
AI Thread Summary
The discussion focuses on calculating the impulse delivered to a soccer ball after it bounces off a player's head. The player analyzes the change in velocity components to determine the impulse's direction and magnitude. Calculations show a magnitude of 3.03 kg·m/s, which aligns with the correct method of using the impulse equation and Pythagorean theorem. A warning is given against oversimplifying the calculation by only considering changes in velocity without proper component analysis. The correct approach emphasizes the importance of using both x and y components to ensure accuracy in future problems.
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Homework Statement


Aplayer bounces a 0.43-kg soccer ball off her head, changing
the velocity of the ball from
Vi = (8.8 m/s)x + (-2.3 m/s)y
to
Vf = (5.2 m/s)xN + (3.7 m/s)y
[/B]
. If the ball is in contact with the
player’s head for 6.7 ms, what are (a) the direction and (b) the
magnitude of the impulse delivered to the ball?

Will I be wrong if I use just change in velocities(ie excluding) in x-comp and y-comp to calculate direction of the impulse.

I did calculation which gave me theta of -59.03, and when using coordinates the theta falls in second quadrant.

Homework Equations


1. delta P(x comp)= Pf(x)-Pi(x)= -1.548
2. delta P(y comp)=Pf(y)-Pi(y)=2.58

The Attempt at a Solution


Using the solutions I calculated magnitude of impulse as 3.03 kg.m/s
 
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That looks about right.
 
So is using just velocities o calculate magnitude acceptable
 
Nkele said:
So is using just velocities o calculate magnitude acceptable
If I understand correctly, you used the equation for the impulse, ##\vec J=m\Delta \vec v## to find the impulse in component form and obtained the magnitude using the Pythagorean theorem. Then you found the angle using the expression ##\theta = \arctan(J_y/J_x)##. That's how you should think of it and it is the correct method. Simplifying it to "using just velocities" is dangerous and could cause trouble next time you encounter something like this.
 
Ok, thank you very much for clarification
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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