A cricket ball $($mass $155$ g $)$ approaches a bat with a velocity of $(-16\mathrm{.}7$hat$(i))\frac{m}{s}.$ While in contact with the bat the force on the ball is shown in the graph, where vec$(F{)}_1=(5\mathrm{.}9$hat$(i))kN,t_1=0\mathrm{.}550ms,$ and $t_2=2\mathrm{.}20ms.$

a$)$ What is the impulse of the ball due to the contact with the bat?

$vec(p)=hat(i)$

b$)$ What is the average force that acted on the ball then?

vec$(F{)}_{\text{a}\text{v}\text{g}}=$

c$)$ What is ball's velocity just after leaving the bat?

vec$(v)=,$hat$(i)$