A $7\mathrm{.}80-g$ bullet moving at $580\frac{m}{s}$ strikes the hand of a superhero, causing the hand to move $5\mathrm{.}00$ cm in the direction of the bullet's velocity before stopping.

$($a$)$ Use work and energy considerations to find the average force that stops the bullet.

N

$($b$)$ Assuming the force is constant, determine how much time elapses between the moment the bullet strikes the hand and the moment it stops moving.

S