Answer
The magnitude of the average force exerted on the ball by the floor is $33.8~N$
Work Step by Step
Any change in the horizontal component of momentum is negligible compared to the change in the vertical component of momentum so we can ignore any horizontal change in momentum.
We can find the change in the vertical component velocity:
$\Delta v = v_f-v_0 = (53~m/s)~sin~18^{\circ}-(-54~m/s)~sin~22^{\circ} = 36.6~m/s$
We can use the magnitude of the change in velocity to find the magnitude of the change in the ball's momentum:
$\Delta p = m~\Delta v$
$\Delta p = (0.060~kg)(36.6~m/s)$
$\Delta p = 2.196~kg~m/s$
The impulse exerted on the ball by the floor is equal to the ball's change in momentum. We can use the impulse to find the average force exerted on the ball by the floor:
$F~t = J$
$F = \frac{J}{t}$
$F = \frac{2.196~kg~m/s}{0.065~s}$
$F = 33.8~N$
The magnitude of the average force exerted on the ball by the floor is $33.8~N$.
