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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...

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.

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