Rocket question in physics?

Question

A rocket car is developed to break the land speed record along a salt flat in Utah. However, the safety of the driver must be considered, so the acceleration of the car must not exceed 5g (or five times the acceleration of gravity) during the test. Using the latest materials and technology, the total mass of the car (including the fuel) is 6000 kilograms, and the mass of the fuel is one-third of the total mass of the car (i.e., 2000 killograms). The car is moved to the starting line (and left at rest), at which time the rocket is ignited. The rocket fuel is expelled at a constant speed of 900 meters per second relative to the car, and is burned at a constant rate until used up, which takes only 15 seconds. Ignore all effects of friction in this problem.

Find the acceleration a_0 of the car just after the rocket is ignited.



Find the final acceleration a_final of the car as the rocket is just about to use up its fuel supply.

Zeta1 · Accepted Answer

This a Diff. equation but I will simplify it a bit:

Apply the "Tsiolkovsky rocket equation"
delta(v) = v(eject) * ln ((mass(initial)/mass(final)) 

delta(v) = 900 * ln (6000 / 4000) = 364.92 m/sec

Now a = v(final) - v(initial) / 15 = 24.2 m/sec^2
since  v(initial) = 0
24.2 m/sec^2 is lower than 5 * 9.8 m/sec^2

The pilot will survive.

kirchwey · Answer

F = v*dm/dt = 900*2000/15 = 120000 N (ref.)
a0 = F/m0 = 120000/6000 = 20 m/s^2
afinal = F/mfinal = 120000/4000 = 30 m/s^2
Both well under the limit of 5g = 49 m/s^2.
EDIT: 2nd answerer correctly calculated the final velocity but then calculated the average acceleration. That's not what the question asked for.

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Rocket question in physics?

2 Answers