EXERCISE 5: COMPARING TO AN ANALYTIC SOLUTION

For the simple case of a lander traveling vertically using only its vertical thruster as it lands, you can derive an analytic function for the lander’s y-velocity as a function of time. Use the following initial conditions for the lander.

Parameter Value
Initial velocity  (m/s)
Initial position  (m)
Mass burn rate  kg/s

If the vertical thrust is constant and is engaged during the entire vertical descent, what is the y-velocity of the lander when it hits the surface of the Moon? Solve the problem analytically. Then, simulate it. Compare the numerical result to the analytic result.

What is the necessary minimum speed of the rocket at its initial position  m so that firing its vertical thruster for the entire descent will cause the rocket to land with nearly zero velocity?