Final answer:
The net force exerted on the ball by the box is calculated by finding the change in momentum and dividing it by the contact time. The calculation yields a net force of -472.12 N, with the direction being opposite to the ball's initial velocity.
Step-by-step explanation:
To calculate the net force exerted on the ball by the box, you first need to find the change in momentum of the ball, which is the mass of the ball times its change in velocity (final velocity minus initial velocity).
Then divide the change in momentum by the time during which the force was applied.
Change in velocity (v) = Final velocity - Initial velocity = -2.0 m/s - (+2.1 m/s) = -4.1 m/s.
Using the formula for change in momentum (\(\Delta p = mv_f - mv_i\)), \(\Delta p = 0.38 kg \times -4.1 m/s = -1.558 kg\cdot m/s\).
Now, to find the average net force (F), we use the equation: \(\Delta p = F \times \Delta t\), where \(\Delta t = 0.0033 s\). Re-arranging the formula to solve for F gives us \(F = \frac{\Delta p}{\Delta t} = \frac{-1.558 kg\cdot m/s}{0.0033 s} = -472.12 N\).
The negative sign indicates that the force is exerted in the opposite direction of the ball's initial velocity.