Two students on roller skates stand face$-$to$-$face, and then push each other away. One student has a mass of $90$ kg ; the other has a mass of $60$ kg $.$ Justify all answers, of course.

$($a$)$ Which student is moving faster?

$M_1{V}_1=M_2{V}_2$

$\frac{90V_1}{90}=\frac{70V_2}{V_2}-7\frac{V_1}{V_2}=\frac{7}{9}$

The magnitude of the first student's velocity to the magnitude of second student's velocity is $7$:$9$

$($b$)$ Which student experienced a larger impulse?

$($c$)$ Which student experienced a larger force?

$($d$)$ Which student experienced larger acceleration?

$($e$)$ Calculate the ratio of the students' velocities just after their hands lose contact. Explain in words how you made this calculation.