Find velocity of the rocket as a function of the time

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A rocket is launched vertically upward from rest in the Earth's gravitational field, near the Earth's surface. The fuel is expelled with a relative speed u with respect to the rocket. Assume the gravitational field is constant. In addition, there is an external time-dependent force that opposes the rocket's motion, with magnitude equal to βt, where t is the time elapsed since the rocket was launched and β is constant. Half of the rocket's initial mass is fuel. Calculate the velocity of the rocket as a function of the time it takes to burn the fuel, until the fuel is spent.

Reference no: EM132688584

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