A rocket is fired vertically upward. The exhaust speed relative to the rocket is u. During a time t, its mass decreases from M $M_0$ to M. Neglect air resistance and take g constant. If its initial speed is zero, its speed after time t is:
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Question

A rocket is fired vertically upward. The exhaust speed relative to the rocket is u. During a time t, its mass decreases from M $M_0$ to M. Neglect air resistance and take g constant. If its initial speed is zero, its speed after time t is:

Options

G1 Physics · Accepted Answer

Choose upward as positive. For a rocket ejecting mass downward, the rocket equation in a uniform gravitational field is M dv = -u dM - Mg dt. Divide by M: dv = -u(dM/M) - g dt. Integrate from initial conditions v=0, M=M0 at t=0 to v, M at time t: v = -u ln(M/M0) - gt = u ln(M0/M) - gt. Correct option: A.

A rocket is fired vertically upward. The exhaust speed relative to the rocket is u. During a time t, its mass decreases from M M 0 M_0 M 0 ​ to M. Neglect air resistance and take g constant. If its initial speed is zero, its speed after time t is:

A rocket is fired vertically upward. The exhaust speed relative to the rocket is u. During a time t, its mass decreases from M M 0 M_0 M 0 to M. Neglect air resistance and take g constant. If its initial speed is zero, its speed after time t is: