- #1

kraigandrews

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## Homework Statement

A rocket ascends from rest in Earth's gravitational field, by ejecting exhaust with constant speed u. Assume that the rate at which mass is expelled is given by dm/dt = −γm where m is the instantaneous mass of the rocket and γ is a constant; and that the rocket is retarded by air resistance with a force mbv where b is a constant.

Determine the velocity of the rocket as a function of time. Here is a hint: The terminal velocity is ( γu−g )/b.

Calculate the time when the velocity is one-half of the terminal velocity.

Data: u = 31.9 m/s; b = 1.2 s−1.

## Homework Equations

dp/dt=F=m(dv/dt)

## The Attempt at a Solution

I get dv=-udm-(g+bv)dt; dm=-γm

so dv=uγ-(g+bv)dt

solving for v:

v(t)=(1/b)e^((-uγ/b)t)-(g/b)

the problem I am running into is what is gamma, because I have no inital condition to apply, and I'm fairly sure the solution to the diff eq is correct.