A rocket for use in deep space is to have the capability of boosting a total load (payload plus the rocket frame and engine) of 3.25 metric tons to a speed of 10,000 m/s. It has an engine and fuel designed to produce an exhaust speed of 2400 m/s. How much fuel plus oxidizer is required (in metric tons)

13.54 tons

Explanation:

Let f be the amount of fuel oxidizer needed

v be the speed

The relationship between them is inverse in nature i.e

f ∝ 1/v

f = k/v

If a rocket for use in deep space is to have the capability of boosting a total load (payload plus the rocket frame and engine) of 3.25 metric tons to a speed of 10,000 m/s, then f = 3.25 when v  = 10,000

Substitute and get k

k = fv

k = 3.25 * 10,000

k = 32500

To get the amount of fuel oxidizer required to produce a speed of 2400m/s, we will find f when v = 2400m/s

Recall that f = k/v

f = 32500/2400

f = 13.54 metric tons

Hence the fuel plus oxidizer that will be required is 13.54 tons

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