A spaceship is pulled toward the ground by gravity. Offsetting this force, the ship fires a rocket directly downward, consuming fuel at a rate of pounds per second and the exhaust material has a constant speed of feet per second relative to the rocket. Find a formula giving the distance the spaceship falls in time if it is at rest at time and has initial weight of pounds.
The motion of the rocket is governed by the equation
We are given
Then, since we have . Therefore,
Then since we have
Hence, the equation of motion is