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For a rocket, the specific impulse was found to be 250s. Given that the thrust force is constant and assuming gravity-free and drag-free conditions, what will the thrust force be for a mass flow rate of the form (4t2-3t) kg/s and a burn duration of 3s?

For a rocket, the specific impulse was found to be 250s. Given that the thrust force is constant and assuming gravity-free and drag-free conditions, what will the thrust force be for a mass flow rate of the form (4t2-3t) kg/s and a burn duration of 3s? Correct Answer 18375 N

Specific impulse Isp = ∫Fdt/(go∫mdt) where m is mass flow rate, go is standard acceleration due to gravity at sea level. Then Isp = Ftb/go(4tb3/3 – 3tb2/2). Using tb = 3s, Isp = 250s, go = 9.8 m/s2, F = 250 x 9.8 x 22.5/3 = 18375 N.

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