the maximum velocity v = -0.0098t + c in R. the rocket fires for t seconds and the velocity of the exhaust is c km/s.

Question

the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel is R. a spacecraft can attain a stable orbit 300km above earth if it reaches a velocity of 7.7 km/s.

A. what is the velocity of a spacecraft whose booster rocket has a mass ratio of sixteen, an exhaust velocity of 3.2 km/s, and a firing time of 40 s?

B. can this rocket attain a stable orbit 300 km above earth? explain in words or show work for how you determined your answer

Answer 1

Hi Isaias. Thankfully, we are given all of the information we need in the problem statement.

We are first given the function that will help us find the velocity (v). Then we are given the mass ratio R which is 16.

In part A, we are given the firing time of 40 s, which is t, as well as the exhaust velocity of 3.2 km/s, which is c.

From there we substitute directly into our function to find the velocity (v).

v = -0.0098(40) + 3.2*ln(16)

So to answer Part A:

v = 8.48 km/s

Part B asks whether the rocket will reach a stable orbit 300 km above earth. This value is defined in the problem statement as 7.7 km/s. Since the rocket reaches an even greater velocity, then yes it will attain a stable orbit.