You are a Rebel Alliance fighter pilot evading pursuit from the Galactic Empire by hovering your space ship beneath the clouds of the planet Cory. Let the positive z direction point upwards and be your ship's position relative to the ground and v be your vertical velocity. The gravitational force is strong with this planet and induces an acceleration (in a vacuum) with absolute value g. The force from air resistance is linear with respect to velocity and is equal to rv, where the drag coefficient r ≤0 is a constant parameter of the model. The ship has mass M. Your engines provide a vertical force. (a) Let L(t) be the input be the vertical lift force provided from your engines.Write down the dynamics for your ship for the position z(t) and velocity v(t). Ignore the scenario when your ship crashes. The right hand sides should contain v(t) and L(t). (b) Given your answer to the previous problem, write down the explicit solution to z(t) and v(t) when the air resistance force is negligible and r = 0. At initial time t = 0, you are 30m above the ground and have an initial velocity of -10m/s. Hint: Write v(t) first then write z(t) in terms of v(t).