[16 marks] A rocket is launched vertically upward with an initial velocity of 80 m/s, so that its height (in meters) after t seconds is given by the function Mt) : 80t 55*. (a) Find an expression for the velocity of the rocket at time t. (b) What is the maximum height achieved by the rocket? (c) What is the velocity of the rocket just before it hits the ground? (d) Sketch the graph of the height function h(t) over the interval 0 g t g 10 seconds. (e) Is the rocket still moving upward or downward at t = 5 seconds? How do you know? Note: For this question, consider the acceleration due to gravity as 10 m / 52, which is a constant. The initial velocity of 80 m/s is upward, and the rocket is launched from the ground at t : 0 seconds. Take into account that the upward direction is positive and the downward direction is negative