A $0\mathrm{.}5$ kg ball, initially moving with a velocity of $10\frac{m}{s}$ due south, collides with a $0\mathrm{.}4$ kg ball that is moving with a velocity of $5\frac{m}{s}$ due east. The collision is perfectly elastic. After the collision, the first ball rebounds with a velocity of $4\frac{m}{s}$ in the $20$ south of east.

a$)$ Draw and label the objects & vectors associated with the motion before collision. $(6$ pts$)$

b$)$ Is the momentum of the system conserved? $(3$ pts$)$

c$)$ Calculate the momentum of the system before and after the collision. $(6$ pts $)$

d$)$ Calculate the impulse experience by the second ball $(0\mathrm{.}4$ kg ball$)$ in the collision $(10$ pts