Problem #54:

In a baseball game, the center fielder throws the ball to home plate so that the ball hits the plate just in time for the catcher to tag the sliding runner. The height of the throw is modeled by the function h(t) = −4.9t + 20t + 1.3, where t is the time after the ball is released in seconds and h(t) is the height of the ball in meters.

a. Find h(0) and explain what the value means in the context of this problem.

b. How long does it take the ball to reach the plate? Show and explain your work.

c. What is the maximum height of the ball? When is the maximum height reached? Show and explain your work.

d. The runner on third base hesitates for half a second and then sprints the 90 ft to home plate, arriving at exactly the same time as the ball. What is the runner’s speed in meters per second? Explain how you found your answer. (Note: 1 in.= 2.54 cm. )

e. Graph y = h(t). Is the graph a good picture of the path of the ball? Explain.

### Recently Asked Questions

- The unimolecular decomposition of urea in aqueous solution is measured at two different temperatures and the following data are observed: (K) T1=333,

- Source SS M F p -value Age 42.667 42.667 17.07 .013 Gender 504.833 168.278 67.31 .004 Age*Gender 38.333 12.778 5.11 .113 Error 40.000 2.500 Total 625.833 Which

- Whether all of these classifications of market ( Developed, Emerging and Frontier) are a good way to determine a country's standing?