1. The problem statement, all variables and given/known data A spacecraft of mass m_{0} is descending with velocity v_{0} to land on an alien plant where the value of g is 1/6 of g on the earth. In order to land safely (meaning the final velocity upon landing is zero), fuel has to be burnt at a constant rate dm/dt=-k, where k is a constant. How far above the surface of the planet should one begin firing the spacecraft (assume constant deceleration) 2. Relevant equations m = m_{0} - kt 3. The attempt at a solution I am trying to use my knowledge of rocket motion. But i am having a hard time picturing the problem. Any comment/help will be great.
starting with v - v_{0} = v_{ex}ln(m_{0}/m) where, v= final velocity v_{0} = initial velocity v_{ex}= exhaust speed relative to spacecraft m_{0}= initial mass m = final mass because final velocity has to be zero and assuming constant exhaust speed, i simplified the above expression to get t. t = m_{0}(e^{-v/vex} -1)/ke-^{v0/vex}