A longer stopping time, a smaller force

A basketball of mass $0.62\ \text{kg}$ comes at you at $8.5\ \text{m/s}$. Catch it with stiff arms and it stings; let your hands move back with it and it does not. You will make the program find the average force for many stopping times, and the shortest time that keeps the force below $60\ \text{N}$.

The idea. Your hands must take away the ball's momentum, $\Delta p = mv$. Spread over a time $\Delta t$, that needs an average force

Your tasks.

1. Work out the momentum your hands must take away.
2. Work out the average force for every stopping time in times.
3. Find the shortest stopping time for which the force is at most $60\ \text{N}$.