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.
