Solution for Question 17
1. Conservation Principles
The total momentum of the system is $P = mu$. Since external forces are zero, $P$ is conserved.
Integral of velocity over time: $\int_0^\tau (v_1 + v_2) dt = u\tau$.
Since distances $s = \int v dt$, we have $s_1 + s_2 = u\tau$, giving $u = \frac{s_1+s_2}{\tau}$.
2. Geometry
If initial positions are $0$ and $l$, and final separation is $x$:
Final Pos 1: $s_1$. Final Pos 2: $l + s_2$.
Separation $x = (l+s_2) – s_1 \implies l = s_1 – s_2 + x$.
Answer: $u = \frac{s_1 + s_2}{\tau}$ and $l = s_1 – s_2 + x$