A pitcher throws a $0\mathrm{.}200$ kg ball so that its speed is $20\mathrm{.}0$ m$/$s and angle is $35\mathrm{.}0$ below the horizontal when a player bats the ball directly toward the pitcher with velocity $50\mathrm{.}0$ 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 $=$

$5\mathrm{.}383$i$+7\mathrm{.}294$j

Write the impulse$-$momentum equations for the horizontal and vertical components of the ball. Make sure to note that the angle of the initial velocity is negative. Combine your results to write the vector equation. Be careful of your signs. 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 $=$

$648$