A rocket of 8kg, including 4kg of fuel takes 35 seconds for the fuel to burn uniformly with no residue and produces a constant thrust of 140 newtons. It takes 35 seconds for the fuel to get spent off leaving gravity and air friction (resistance) to be the only forces acting on the rocket. If the air resistance is 0.02v2. Write initial value problems to determine the velocity of the rocket, with t being a function of time for (a) 0 ≤ t ≤ 35 (b) 35 ≤ t ≤ T, where T is the time the rocket reaches its maximum altitude, and for (c) T ≤ t ≤ Ti, where Ti is the time the rocket hits the ground.