A test rocket is launched (zero initial velocity) in the desert at an initial height of 832 meters above sea level. The initial mass is 3380 kilograms and the final mass, after the solid fuel is burned, is 2440 kg. The rocket engine will burn for about 10.3 seconds. At the initial altitude above sea-level, the thrust of the engine is 153,510 Newtons. Assume a coefficient of k = 0.43 for drag. a) Assuming the initial height of h0 = 832 meters, integrate the velocity function to find a function for height during the launch. b) What does the model predict as the height at 10 seconds and at 11 seconds?