Question

A booster rocket for a spacecraft has a firing time of 30 seconds, an exhaust velocity of 2.1 km/s, and a mass ratio of about 15. Find the maximum velocity of the spacecraft.

a) 31.5 km/s

b) 41.0 km/s

c) 51.2 km/s

d) 61.7 km/s

Answer 1

The maximum velocity of the spacecraft is approximately 10.8 km/s.

Step-by-step explanation:

To find the maximum velocity of the spacecraft, we can use the rocket equation which relates the exhaust velocity, the mass ratio, and the natural logarithm of the initial to final mass ratio:

v_max = v_e * ln(m_i/m_f)

Given that the exhaust velocity (v_e) is 2.1 km/s and the mass ratio (m_i/m_f) is 15, we can substitute these values into the equation:

v_max = 2.1 km/s * ln(15)

Using a logarithmic calculator, we find that v_max is approximately 10.8 km/s. Therefore, the maximum velocity of the spacecraft is not among the provided multiple-choice options.