NASA designed the New Horizons mission to Pluto to be on the fastest rocket ever launched to ensure the space-craft arrived at Pluto within ten years of launch. The thrust

of the launch vehicle was 1.10x107 newtons, and its initial mass, including fuel was 5.75x105 kg. The exhaust gases moved at a speed 5.00x103 m/s from the rocket towards the ground throughout. A. Draw a diagram illustrating the forces acting on the rocket immediately after launch. B. Calculate the initial acceleration of the rocket (t=0). Hint: use the diagram from part A. C. Calculate the mass-loss rate (burn rate) as the rocket fuel is burned. D. Calculate the time that half of the total initial mass is lost. Hint: when mass is burning M(t)=M_{0}-\frac{d M}{d t} t . Calculate the acceleration of the rocket at this time (thalf-mass). Hint: use the diagram from part A.