**Problem P2. **(Propulsion) (L.O. A & B)

There is a test facility at NASA Langley Research Center where a hydraulic catapult is used to accelerate vehicles. It provides an instructive illustration of the integral momentum theorem.

a) Explain what each term in the equation of motion represents.

b) Derive an equation of motion for the airplane acceleration (dV(t)/dt) as
a function of the velocity, area, and density of the water jet (Vj, Aj and rj
respectively), and the mass (m) and velocity (V) of the airplane. Neglect the
effects of gravity and assume the forces associated with the air around the
vehicle and launcher are small compared to those associated with the water jet.
Assume the mass of water in contact with and accelerating the bucket is negligible
relative to M so you can neglect any change with time of the momentum of the
jet within the control volume.

c) What is the thrust, T, on the airplane?