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The troublesome Mooninites Ignignokt and Err have stolen a rocket from

NASA and escaped to Mars. On Mars, Err opens the classified instruction

documents and learns that this is no ordinary rocket but one with an experimental

engine that provides a time-dependent thrust for exactly 10 seconds after which the

engines shut off completely. The thrust provided by the rocket engines can be

expressed as F(t) = −24t 2 +144t

and is purely in the vertical direction. Up to no good as usual, they decide to fire off

the rocket from the surface of Mars. Neglecting air resistance and assuming the

rocket has a mass of 2kg, how long is the rocket airborne before it crashes back to

the ground and what is the rocket’s maximum elevation?

The Thrust equation (having a negative involved) is messing everything in my equation up. According to my professor this problem should only take me five minutes, but I've spent the last two hours doing velocity and accleration for each and every second as well as for the problem itself, and nothing is getting me anywhere. Any assistance in helping me keep my sanity would help a ton! Thanks for you time guys.