Assignment:
Bob the Iguana is waiting to use his Giant Slingshot to shoot the Evil Bart the Blackbird out of the sky as he flies overhead. Bob's Giant Slingshot launches a stone vertically so that the function h(t) = 300t — 16t^2 models the height h in feet of the stone t seconds after it leaves the slingshot. Answer each of the following questions using algebra and/or calculus (and showing your work). Using a formula from your physics class is not an answer that uses calculus! Use at least 3 decimal places in your answers and don't forget limits.
(a) Bart the Blackbird is ?ying at a constant height of 1/4 of a mile and constant speed of 10 ft/sec. Assuming that Bob tima his shot correctly, can he hit Bart? Explain using complete sentences how you know.
(b) Now assume that Bart ?ies at a constant height of 1000 feet and constant speed of 10 ft/sec. When should Bob release the slingshot so that he can knock Evil Bart the Blackbird out of the sky? Explain how you know. (Complete sentences expected).
(c) With what velocity will the stone hit Bart? How do you know?
(d) Suppose Bob misses. How long does Bob the Iguana have to get out of the way before the stone he shot from the slingshot returns to the ground and hits him? How do you know.
(e) With what velocity will the stone hit the ground?
Provide complete and step by step solution for the question and show calculations and use formulas.