Robert has just bought a new model rocket, and is trying to measure its flight characteristics. The rocket engine package claims that it will maintain a constant thrust of 13.8 N until the engine is used up. Robert launches the rocket on a windless day, so that it travels straight up, and uses his laser range-finder to meaure that the height of the rocket when the engine cuts off is 14.6 m. He also measures the rocket/'s peak height, which is 19.1 m. If the rocket has a mass of 0.663 kg, how much work is done by the drag force on the rocket during its ascent?

You must assume that the mass of the rocket and engine remains constant - even though the engine is burning.

You know the engine produces 13.8N for a distance of 14.6m

The total energy expended (work done) by the engine is FxD so you can calculate that

Now - some of that is given to the rocket as kinetic and potential energy, and some is expended against the drag force.

At the peak of its flight ALL the energy given to the rocket is potential energy (its velocity is zero) and that is calculated as mgh

So

Energy given to rocket = mgh

Energy expended by engine = F x D (D = height where engine stops)

Energy 'lost' to drag is the difference between the two values.