Agnikul Cosmos interview question

Q:Write down the equations of motion assuming gravity loss, drag, and engine thrust based accelerations on a single stage rocket from vertical launch to burnout. Assume a thrust of 100kN produced by the engine, thrust to weight ratio of 1.4 Initiate a gravity turn at approximately 100 meters altitude and capture the dynamics of the rocket including the impact of the gravity turn. Plot the trajectory, dynamic pressure and other key variables.