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## Homework Statement

A rocket sled moves along a horizontal plane, and is retarded by a friction force friction = μW, where μ is constant and W is the weight of the sled. The sled’s initial mass is M, and its rocket engine expels mass at constant rate dM/dt ≡ γ; the expelled mass has constant speed v0 relative to the rocket. The rocket sled starts from rest and the engine stops when half the sled’s total mass is gone. Find an expression for the maximum speed.

## Homework Equations

d(mv)/dt = F(x)

## The Attempt at a Solution

To solve the problem, I found the differential equation for momentum, taking the momentum at a point in time and then the momentum a moment later, then dividing by a change in time.

This interpretation worked.

This interpretation did not work.

I don't understand why the second interpretation does not work.

Thanks