A Rocket accelerates by burning its onboard fuel, so its mass decreases with time....?

Question

A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity ve (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation below where g is the acceleration due to gravity and t is not too large.

v(t)=-gt-ve[(m-rt)/m]

If g = 9.8 m/s2, m = 30000 kg, r = 135 kg/s, and ve = 3000 m/s, find the height of the rocket one minute after liftoff.


((i don't even know where to start....))

Answer 1

Forget all the gobbledygook about the physics, and just concentrate on the math. They have given you a formula for the velocity as a function of time; that's 90% of what you need.

The other 10% is this: You should know that if you take the integral of velocity (with respect to time), you get another function which gives DISTANCE (in this case, height) as a function of time.

So, integrate that sucker. Then plug in t=1 min., and the given values of g, r, m, etc. into the equation.

Answer 2

put in the values you know, then integrate V(t) in respect to time

the integral equals the height, so substitute 60 seconds in for t and thats your answer