The formula h() = 162 + 480 , describes a model rocket's height. h() is the rocket's height measured in feet from the ground, seconds after take-off.

(a)Sketch the graph of h() for 0. After how many seconds does the rocket impact the ground?

(b)Find the velocity function () of the rocket.

(c)Sketch the graph of () and interpret it based on the rocket's actual motion.

(d)Compute the rocket's velocity at = 0, = 15, and = 18. How do you interpret the signs

of the values you obtained?

(e) Sketch the graph of (), the speed function. Find the rocket's speed at = 0, = 15, and = 18.

(f)After how many seconds will the rocket start falling? Use differentiation to find the

maximum height attained by the rocket.

(g)After how many seconds will the rocket hit the ground? What is its velocity at that moment?

(h)Determine the rocket's acceleration, (). Why does it make sense that () is constant and

negative? Explain.