A rocket is traveling through space with no gravitational fields on its way to resupply a spacecraft. The
rocket has two stages. It will burn through stage-1 then stage-2 to reach a cruising speed of 13,000 m/s.
After this, the rocket will use the remaining fuel to turn around and reduce the speed to the spacecraft's
speed of 11,000 m/s. The rocket's initial speed is 400 m/s and the initial mass is $m_0$. The total fuel
available is 0.75($m_0$) and 0.35($m_0$) is needed for the stage-1 burn. The rest of the fuel is needed to reach
max speed after the stage-2 burn and slowing down to reach the spacecraft's speed. After stage-1, the
rocket will release a stage-1 structure. The mass of just the stage-1 structure released is $m_1 = 0.1(m_0)$.
Assume all motion occurs in a straight line.
1. What is the velocity after stage-1?
2. How much fuel remains after the rocket reaches its cruising speed?
3. As the rocket gets close to the spacecraft, it will turn around and fire it's engine to provide
thrust in the opposite direction to slow down. Does the rocket have enough fuel remaining to
match the spacecraft's speed of 11,000m/s? If so, how much fuel is remaining? If not, what is
the final velocity of the rocket after all the fuel is spent?