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Problem

The missile weighs 40000 lb. The constant thrust …

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Problem 138 Easy Difficulty

The second stage of a two-stage rocket weighs 2000 lb (empty) and is launched from the first stage with a velocity of $3000 \mathrm{mi} / \mathrm{h}$. The fuel in the second stage weighs 1000 Ib. If it is consumed at the rate of $50 \mathrm{lb} / \mathrm{s}$ and ejected with a relative velocity of 8000 ft/s, determine the acceleration of the second stage just after the engine is fired. What is the rocket's acceleration just before all the fuel is consumed? Neglect the effect of gravitation.

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Video Transcript

in this problem. We have a two stage rocket with a given weight, and we know the rate in which fuel is being consumed and ejected. Now we need to determine declaration off the second stage of the rocket just after the Indian is fired and the rockets acceleration just before all the fuel is consumed. So in the initial case, just after the engines fired, we know that using the steady flow equations at the sum of all the forces acting on this rocket was equal to M D v D P minus the D E, which is the relative rate at which, if you are moving, I'm Yeah, the math floor it off dejected fueled the M E T T. So we know that if we assume that they waited negligible, there's no forces acting on the rocket. It's math is 2000 plus £1000 for the £3000 which is its weight over G 32.2 and DVD T is the acceleration of the rocket A. But this is minus 8000 feet, the second and a florid off £50 per second so that 50 divided by G convert that to a math. And so if you rearrange the equation, we get that the acceleration just after the engine is fired is 133 feet, the square second. That was initially now, finally, just before all the fuel is consumed, we use the steady flow equation again, and we have that the forces be some of the forces acting on the rocket, which is zero. Now all the fuel is consumed to the masses. Only that off the the rocket, which is £2000 over 32.2 times a Miami, 8000 until 50 over again, 32.2. And if you rearrange this, we get the information off the rocket finally to be 200 feet the square second.

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