Answer to Question #292320 in Mechanics | Relativity for Lil

Question

A boat moves at 10.00 m/s relative to the water. If the boat is in a river where the current is 2.00 m/s, how long

does it take the boat to make a complete round trip of 999 m upstream followed by another 999-m trip

downstream?

Answer 1

The boat at speed v moves against the current of speed u with velocity v-u relative to the earth, and downstream with the relative velocity of v+u.

So, the time of the trip is

$$t=\dfrac d{v-u}+\dfrac d{v+u},\\\space\\ t=\dfrac{2vd}{(v+u)(v-u)}=208\text{ s}.$$