I Don't Know How to Solve This Physics Problem

Question

Engineers are designing a rocket to be used in deep space. If the rocket is fired from rest in deep space, the total mass of the rocket, payload, and unspent fuel must reach a speed of 1.25 ✕ 10⁴ m/s in order to accomplish other maneuvers. Due to the amount of fuel which is still onboard, the rocket, payload, and unspent fuel will have a final mass of 4.00 ✕ 10³ kg. If the design of the rocket is such that the exhaust speed is 2.85 ✕ 10³ m/s, determine the amount of fuel required to perform this maneuver.

Answer 1

Hi Elle B., Nonsense. You do so know how to solve this problem. Physics dynamics problems are either about energy or momentum. If you think about your given data, momentum (P) should seem the way to go. P(initial) = 0 b/c everything is at rest. You are given a mass and a speed for the rocket portion of P(final). That allows you to figure a momentum. That momentum MUST exactly balance the momentum of the ejected fuel. You know the "speed" of the ejected fuel, so calculate the mass.

I can see where you might have gotten alarmed because the fuel is ejected at 2.85 * 10^3 m/s, but you want the rocket ship to move at 1.25 * 10^4 m/s in the opposite direction. So the ejected fuel is trailing the rocket? Isn't the whole point of burning the fuel to get it to go far away?

Yes the ejected fuel is trailing the rocket (after a while of acceleration), as it appears to a stationary observer. But think of it this way: the fuel ejection speed operates to push the ejected fuel and the rocket apart. So you may just take the fuel momentum transfer as in the rocket's frame of reference, but the effect on the rocket as in the stationary frame of reference.

Quite a bit of fuel, isn't it.

--Cheers, --Mr. d.