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Member has been reminded to provide typed text instead of barely readable pictures.

## Homework Statement

Freight car and hopper*

An empty freight car of mass M starts from rest under an applied force F. At the same time, sand begins to run into the car at steady rate b from a hopper at rest along the track.

Find the speed when a mass of sand m has been transferred.

## Homework Equations

attached

## The Attempt at a Solution

attached

The solution answer has an extra b*t in the denominator and + answer. Where is the flaw in my method? Now I understand this can be done shorter using impulse and exact values but I prefer the more general approach and deduce specific cases at the end. Thanks