A $7\mathrm{.}80$ g bullet is initially moving at $540$ m$/$s just before it penetrates a tree trunk to a depth of $5\mathrm{.}40$ cm$.$

$($a$)$

What is the magnitude of the average frictional force $($in N$)$ that is exerted on the bullet while it is moving through the tree trunk? Use work and energy considerations to obtain your answer.

N

$($b$)$

Assuming the frictional force is constant, how much time $($in s$)$ elapses between the moment the bullet enters the tree trunk and the moment it stops moving?

s