spacecraft landing on an alien planet

squarky

1. The problem statement, all variables and given/known data

A spacecraft of mass m₀ is descending with velocity v₀ 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 = m₀ - 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.

squarky

starting with
v - v₀ = v_exln(m₀/m)

where,
v= final velocity
v₀ = initial velocity
v_ex= exhaust speed relative to spacecraft
m₀= 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 = m₀(e^-v/v_ex -1)/ke-^v₀/v_ex