The two objects shown in the figure collide with each other: Object A has a mass of $0\mathrm{.}4$ kg and an initial speed of $25\frac{m}{s}.$ Object B has a mass of $0\mathrm{.}6$ kg and an initial speed of $20\frac{m}{s}.$ After the collision object A has a speed of $v_{A,f}$ and is moving at an angle ${}_A$ relative to its original direction of motion, and object $B$ has a speed of $v_{B,t}\frac{m}{s}$ and is now moving at an angle of ${}_B$ relative to its original direction of motion.

A$.$ What is the change in momentum of the system in the $x$ direction during the collision? $(2)$ points$)$

B$.$ What is the change in momentum of the system in the $y$ direction during the collision? $(2$ points$)$

C$.$ If ${}_A=40$ and ${}_B=30,$ what is $v_{A,\text{I}}?$ Include all of your work. $(4$ points$)$

D$.$ What is your answer to part C$?(1$ point$)$

E$.$ Briefly explain how you solved part C$.(1$ point$)$