Question

Two ships are 10 km apart on a line joining south to north. The one farther north is steaming west at $20km{h}^{-1}$. The other is steaming north at $20km{h}^{-1}$. What is their distance of closest approach? How long do they take to reach it?

Answer 1

solving from the frame of particle 1,

We get $d_{short}=10\cos {45}^o$

$=\frac{10}{\sqrt{2}}=5\sqrt{2}km$

$t=\frac{10\sin 45}{|\overline{V_{21}|}}=\frac{10\times 1/\sqrt{2}}{20\sqrt{2}}$

$=\frac{1}{4}h=15min$