You've just received your new Scooty-Puff, Jr. Space scooter in the mail and you hope to use it to travel from Earth to Mars. The specification sheet that came with it says that it will provide a time dependent thrust given by the equation below. Assume the mass of Scooty-Puff Jr. you and the scooter combined is 500 kg and a negligible amount of mass is lost during the acceleration. Also assume you are taking off from a space station, so gravitational forces can be ignored.

(a) This equation doesn't show units but there must be some "buried in the 3/400 part of the expression. Use Dimensionality sense-making to determine what units must be associated with the 3/400 part of the term.

(b) Make a detailed plot of the thrust up to 3300 seconds.

(c) Approximately what is the maximum acceleration the scooter obtains?

(d) Use the Known Values sense-making technique to test the safety of your answer in part (c). The fine print in the manual says that after the scooter has reached maximum thrust, it will shut off once the thrust is back down to 1% of the maximum.

(e) At approximately what time will the thrusters shut off? (1) With your approximation in part

(e), how long will it take to reach Mars? (hint: Ignore the rocket firing stage)

(g) Why can you safely ignore the rocket firing stage and still get a reasonable approximation?

(h) Extra-credit. calculate the exact impulse delivered during the thrust.