The Apollo Lunar Module was employed to make the transition from the space-craft to the surface of moon and back. Consider an alike module for landing on the surface of Mars. Employ conservation of mechanical energy to answer given questions.
(i) As the lander is downward, if the pilot decides to shut down the engine if the lander is at a height of 1.8 m, (this might not be a safe height to shut down the engine) and the velocity of the lander (relative to the surface of planet) is 1.7 m/s then what will be velocity of the lander at impact?
Note: g on the surface of mars is around 0.4 times that on the surface of Earth.
(ii) In case of the lunar module an impact velocity of 3.0 m/s or less was necessary for a safe landing. Supposing this to be the case for Mars lander as well, at what maximum height could the pilot shut down the engines to make sure a safe landing? Suppose the velocity v0 at the time the engine is shut down is 1.7 m/s.