The first stage of a space vehicle consumed fuel and oxidizer at the rate of 1.75 x 104 kg/s, with an exhaust speed of 2.40 x 103 m/s. Find the acceleration (in m/s2) of the vehicle just as it lifted off the launch pad on the Earth, if the vehicle's initial mass was 3.00 x 106 kg. (Note: You must include the force of gravity to solve the problem.)

Explanation:

In order to solve this problem, we must first draw a free body diagram of the situation. (See attached picture)

from this diagram, we can do the following sum of forces:

where m is the mass of the rocket and a is its acceleration.

where is the force of exhaust. We can solve this for the acceleration, so we get:

we can find the force of exhaust by using the momentum formula:

Ft=mv

so we can solve this for the force:

the problem already tells us what m/t is equal to, so we can directly substitute:

which yields:

So we can now substitute:

so:

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