A soccer ball player bounces the ball off her head, changing the velocity of the

Question

A soccer ball player bounces the ball off her head, changing the velocity of the ball. She changes the x component of the velocity of the ball from vix = 8.5 m/s to vfx = 4.6 m/s and the y component from viy =

m/s to vfy = 4.4 m/s. If the ball has a mass of 0.43 kgand is in contact with the player's head for 7.1 ms, determine the following.

(a) direction of the impulse delivered to the ball
° counterclockwise from the +x-axis

(b) magnitude of the impulse delivered to the ball
kg · m/s

A soccer ball player bounces the ball off her head, changing the velocity of the ball. She changes the x component of the velocity of the ball from Yx = 8.5 m/s to Y = 4.6 m/s and the y component from Vy =-2.1 m/s to vfy = 4.4 m/s. If the ball has a mass of 0.43 kg and is in contact with the player's head for 7.1 ms, determine the following. (a) direction of the impulse delivered to the ball o counterclockwise from the +x-axis (b) magnitude of the impulse delivered to the ball kg m/s

Explanation / Answer

Impulse is change in momentum.

J = m(vxf - vxi)x + m(vyf - vyi)y

=(.43)(4.6 - 8.5)x + (.43)(4.4 + 2.1)y

= (-1.677)x + (2.795)y

This impulse vector lies in the 2nd quadrant. You can get the angle it makes with the neg x-axis by;

Tan(L) = 2.795/1.677 = 1.66
L = 59 deg

Then the angle it makes with the positive x-axis is;

180 - 59 = 121 deg

The magnitude is just;

IJI = SqRt[Jx^2 + Jy^2] = SqRt[(-1.677)^2 + (2.795)^2] = 3.259 kg-m/s

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