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## Homework Statement

A ship's engine supplies power of 85MW, which propels the ship of mass 5.3×106 kg across the sea at its top speed of 11##ms^{−1}##. The frictional force exerted on the ship by the sea is directly proportional to its speed. If it starts at top speed and then travels in a straight line, how far will it go after the engines stop?

## Homework Equations

## The Attempt at a Solution

I thought the ship would start of with energy ##\frac{1}{2}mv^2##, and that the work done by friction has to equal this amount for the ship to stop. It says friction is proportional to speed and from dimensional analysis I need units of kgm##s^{-2}##, mass and time also have to be included in the equation for friction, and it has to be inversely proportional to time so that ##F = \frac{mv}{t}## and work done ##= \int F dx = \frac{mvx}{t}##. There should probably also be some kind of constant of proportionality in there.

Equating the two energy equations gives me ##x = \frac{vt}{2}## but I don't know t, so that's no good. And I don't know what else to try. Thanks for any help!