A rocket of total mass M and with burnout mass 0.20M attains a speed of 3 400 m/s after starting from rest in deep space.What is the exhaust velocity of the rocket?
A)6.8E+2 m/s
B)2.1E+3 m/s
C)1.7E+4 m/s
D)2.2E+3 m/s
E)1.1E+3 m/s

Question

Quizplus · Accepted Answer

The exhaust velocity can be found using the rocket equation, which is $v = v_e \ln(\frac{M}{M_f})$, where $v$ is the final velocity of the rocket, $v_e$ is the exhaust velocity, $M$ is the initial mass of the rocket, and $M_f$ is the final mass of the rocket. Given that the final mass is $0.20M$, we can rearrange the equation to solve for $v_e$: $v_e = \frac{v}{\ln(\frac{M}{M_f})}$. Substituting the given values, $v_e = \frac{3400}{\ln(\frac{M}{0.20M})} = \frac{3400}{\ln(5)} \approx 2100$ m/s.

A Rocket of Total Mass M and with Burnout Mass