A pitcher throws a $0\mathrm{.}200$ kg ball so that its speed is $14\mathrm{.}0$ m$/$s and angle is $35\mathrm{.}0$ below the horizontal when a player bats the ball directly toward the pitcher with velocity $48\mathrm{.}0$ m$/$s at $30\mathrm{.}0$ above the horizontal. Assume $+$ to be along the line from the batter to the pitcher and $+$ to be the upward vertical direction. $($Express your answers in vector form.$)$

$($a$)$

Determine the impulse $($in N $$ s$)$ delivered to the ball.

I $=$

N $$ s

$($b$)$

If the force on the ball increases linearly for $4\mathrm{.}00$ ms$,$ holds constant for $20\mathrm{.}0$ ms$,$ and then decreases linearly to zero in another $4\mathrm{.}00$ ms$,$ what is the maximum force $($in N$)$ on the ball?

Fmax $=$

N