Calculus

A baseball is hit 3 feet above home plate at a angle with the horizontal. Its initial speed is
100 feet per second. The path of the baseball at any time (in seconds) is given by the parametric
equations
and
Exercises
1. Find
2. At what time is the ball at its maximum height?
3. What is the maximum height of the ball?
4. When the ball is at its maximum height, what is its vertical velocity?
5. When the ball is at its maximum height, what is its horizontal velocity?
6. How long is the ball in the air?
7. How far is the ball from home plate when it hits the ground?
8. Find the value of at the instant the ball hits the ground. What does this mean in the context
of the problem?
9. What is the vertical velocity of the ball at impact?
10. What is the horizontal velocity of the ball at impact?
11. A 14-foot fence is located 300 feet from home plate. Will the ball clear the fence? Explain.
12. Set up a definite integral to determine the total length of the path traveled by the ball.
13. Use a graphing utility to evaluate the integral you wrote in Exercise 12. Compare this to your
answer from Exercise 7.
14. Find a rectangular equation for the position of the ball by eliminating the parameter
15. Find the derivative of the function you wrote in Exercise 14.
16. According to the rectangular equation, for what value of is the ball at its maximum height?
17. Use your answer from Exercise 16 and the equation to find when the ball is
at its maximum height. Compare this to your answer from Exercise 2.
18. Why is it beneficial to express the path of the baseball with parametric equations rather than a
rectangular equation? Explain.

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