a 57 g tennis ball is traveling at 45 m/s to the right, when it hits a racket. the ball reverses direction…

Explanation:

Step1: Calculate the initial and final momentum

The mass of the ball $m = 57\ g=0.057\ kg$, initial velocity $v_1 = 45\ m/s$ (right - positive), final velocity $v_2=- 33\ m/s$ (left - negative). Initial momentum $p_1 = mv_1=0.057\times45\ kg\cdot m/s = 2.565\ kg\cdot m/s$, final momentum $p_2=mv_2 = 0.057\times(-33)\ kg\cdot m/s=-1.881\ kg\cdot m/s$.

Step2: Calculate the change in momentum

The change in momentum $\Delta p=p_2 - p_1=-1.881 - 2.565=-4.446\ kg\cdot m/s$. The magnitude of the change in momentum $|\Delta p| = 4.446\ kg\cdot m/s$.

Step3: Use the impulse - momentum theorem

The impulse - momentum theorem states that $J=\Delta p = F\Delta t$, where $J$ is the impulse, $F$ is the force and $\Delta t$ is the time of contact. Given $\Delta t = 0.0085\ s$. We can solve for $F$: $F=\frac{|\Delta p|}{\Delta t}=\frac{4.446}{0.0085}\ N\approx523\ N$.

Answer:

520 N (closest value to the calculated result)