question_answer 25)

A rocket is fired vertically from the surface of Mars with a speed of 2 km  If 20% of its initial kinetic energy is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of Mars before returning to it. Mass of Mars radius of Mars = 3395 km ;                                                     

Answer:

Let m = mass of the rocket, M = mass of the Mars and R = radius of Mars. Let  be the initial velocity of rocket.                 Initial K.E.                                                                                                                                                                                                                                                                                                                     Initial P.E.                                                                                                                                                                             Since, 20% of K.E. is lost, only 80% is left behind to reach the height. Therefore,                        Total initial energy available  If the rocket reaches the highest point which is at a height h from the surface of Mars, its .K.E. is zero and Using principle of conservation of energy, we have Or Or   Or Or