You are traveling...

C. Sketch the graph of v(t) and interpret it based on the rocket's actual motion. d. Compute the rocket's velocity at t = 0, t = 15, and t = 18. How do you interpret the signs of the values you obtained? sketch the graph of s(t), the speed function. Find the rocket's speed at t = 0, t = 15, and t = 18. f . After how many seconds will the rocket start falling? Use differentiation to find the maximum height attained by the rocket. After how many seconds will the rocket hit the ground? What is its velocity at that moment? h. Determine the rocket's acceleration, a(t). Why does it make sense that a(t) is constant and negative? Explain. 2. You are traveling down a country road at a rate of 95 feet/sec when you see a large cow 300 feet in front of you and directly in your lane. The cow is fearless, and staring you down. (Or perhaps she does not understand the gravity of the situation.) Regardless, if you simply hit your brakes, after t seconds, the car will be j(t)=95t-9t^2 feet from the point where the brakes were first applied. (i) Must you steer to avoid the cow, or can you rely solely on your brakes? Explain. (ii) Graph j(t), j'(t), and j"(t) and interpret their meanings in context. (iii) Is there a time t after which the graphs in part (ii) probably do not accurately model the path of the car? (iv) Write a piece-wise function using j(t) that would more accurately model the path of the car on the (0. 101