Question

# Mark Watney, of The Martian fame, has somehow gotten himself stuck on another, this time unknown,...

Mark Watney, of The Martian fame, has somehow gotten himself stuck on another, this time unknown, planet. You need to help him perform some calculations so that he can, once again, escape the planet’s surface and return to Earth. Here’s what Mark knows: ▪ He has a mass of 77.5 kg and has found a capsule to launch in that has a mass of 2542 kg. ▪ He is definitely still in our solar system. ▪ On the surface, he found a big stone tablet proclaiming that the planet has a radius of 6042km, an acceleration due to gravity of 8.70 m/s2 [down] and a “year” of 1406 “days” – the part of the tablet dealing with the length of a day was missing ▪ By using his watch to track the time between 2 consecutive “noons”, he found the length of one day is 22.5h.

6. Bored while waiting for his rescue ship to arrive, Mark fixes up a dune buggy (554kg) he found partially buried in the sand. While cruising along at a velocity of 8.50m/s [north], he collides with a boulder (889kg) that was rolling at 12.2m/s [east] in an elastic collision. After the collision, Mark has a velocity of 6.70m/s [72o east from north]. Determine the velocity of the boulder after the collision.

8. Mark determines that he should launch himself into geosynchronous orbit around the planet so that he doesn’t float off into space while waiting for the ship. Geosynchronous means he stays at the same point above the planet all the time. How far would this put him above the surface of the planet? (Hint: if he stays at the same point, what would his orbital period be?)

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