Homework Help: Rocket in space

1. Oct 18, 2004

ElectricMile

A rocket is fired in deep space, where gravity is negligible. In the first second it ejects (1/160) of its mass as exhaust gas and has an acceleration of 15.3 m/s^2.

What is the speed V(gas) of the exhaust gas relative to the rocket?

2. Oct 18, 2004

ElectricMile

can anyone help me out?

3. Oct 18, 2004

Tide

Does this equation look familiar to you?

$$v = v_e \ln \frac {M_0}{M}$$

4. Oct 19, 2004

HallsofIvy

More fundamentally, use conservation of momentum. Take the initial values of the mass and speed of the rocket to be M and v. The initial momentum is Mv. After ejecting (1/160)M, the rocket's mass is (159/160) M. Since it accelerated at 15.3 m/s2 for 1 sec. , it gained 15.3 m/s: it's final speed is v+15.3 and it's final momentum is (159/160)M(v+15.3). The expelled gas has mass (1/160)M and, with velocity -V (opposite to the direction of the rocket) so its momentum is -(1/160)MV.

By conservation of momentum, we must have
(159/160)M(v+15.3)- (1/160)MV= Mv. I don't see any way of solving for V without knowing v (just as Tide's equation required ve).

5. Oct 19, 2004

Clausius2

Hey Hallsofivy! Now I've noticed you don't ask the famous adage "What have you done till now?" and "show me what you've done!".

Times are changing....(nostalgia... )