Unless otherwise stated, in the following problems we assume that the gravitational...

Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec² in the MKS system and g = 32 ft/sec² in the U.S. Customary System.

Rocket Flight. A model rocket having initial mass m0 kg is launched vertically from the ground. The rocket expels gas at a constant rate of kg/sec and at a constant velocity of β m/sec relative to the rocket. Assume that the magnitude of the gravitational force is proportional to the mass with proportionality constant g. Because the mass is not constant, Newton’s second law leads to the equation

Where v = dx/dt is the velocity of the rocket, x is its height above the ground, and