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 = 8.1 m/s to vfx = 4.7 m/s and the y-component from viy = −3.3 m/s to vfy = 3.2 m/s. If the ball has a mass of 0.44 kg and is in contact with the player's head for 7.1 ms, determine the following. (a) direction of the impulse (in degrees counterclockwise from the +x-axis) delivered to the ball ° counterclockwise from the +x-axis (b) magnitude of the impulse (in kg · m/s) delivered to the ball kg · m/s

Answer 1

The change in horizontal velocity is (4.7 - 8.1) = -3.4 m/s

The change in vertical velocity is (3.2 + 3.3) = 6.5 m/s

These are the components of velocity DELIVERED to the ball by the player's pretty head during the collision.  

The magnitude of the change in velocity is √(-3.4² + 6.5²) = 7.336 m/s .

The magnitude of the ball's change in momentum is (m · v) = (0.44 · 7.336) = 3.228  kg-m/s .

==> The change in the ball's momentum is exactly the impulse during the collision. . . . . . 3.228 kg-m/s .

==> The direction of the impulse is the direction of the change in momentum:  (-3.4)i + (6.5)j

The direction is  arctan (6.5 / -3.4)  =  -62.39°

That's clockwise from the +x axis, which is roughly "southeast".  The question wants it counterclockwise from the +x axis.  That's (360-62.39) =

Direction of the impulse = 297.61°

We know that impulse is equivalent to the change in momentum, and that's how I approached the solution.  Impulse is also (force x time) during the collision.  We're given the time in contact, but I didn't need to use it.  I guess I would have needed to use it if we were interested in the FORCE she exerted on the ball with her head, but we didn't need to find that.