- #1

Karol

- 1,380

- 22

## Homework Statement

A rocket launches from a space base at 0 velocity and looses mass at constant rate C. what is the ratio between the rocket's mass at maximum momentum to it's initial mass.

## Homework Equations

Newton's second law: ##F=dP=\frac{d(mV)}{dt}##

Conservation of momentum: ##m_1v_1=m_2v_2##

## The Attempt at a Solution

To find maximum momentum i differentiate momentum:

$$F=dP=\frac{d(mV)}{dt}=m\frac{dV}{dt}+V\frac{dm}{dt}=ma+V\cdot C=0$$

$$m(t)a(t)=-C\cdot V(t),\ m=M_0-C\cdot t\rightarrow (M_0-C\cdot t)a(t)=-CV(t) \rightarrow t=\frac{M_0}{C}+\frac{V(t)}{a(t)}$$

Both a(t) and V(t) are functions of T and i can't solve for t.

I am not told anything about the velocity the mass leaves the rocket.