A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function h left parenthesis t right parenthesis equals negative 4.9t squared plus 14.7t plus 1h (t) = - 4.9t2+14.7t+1.

How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?

Question

Mathematics

Mara Chen

16 May, 23:52

A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function h left parenthesis t right parenthesis equals negative 4.9t squared plus 14.7t plus 1h (t) = - 4.9t2+14.7t+1.

How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?

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Answers (1)

Know the Answer?

Kailyn Houston · Answer 1

To solve for the time it reach the maximum height, you must solve the first derivative of the function and equate it to zero

h (t) = - 4.9t^2 + 14.7t + 1

dh / dt = - 9.8t + 14.7

then equate to zero

-9.8t + 14.7 = 0

solve for t

t = 1.5 s

then the maximum height is when t = 1.5

h (t) = - 4.9t^2 + 14.7t + 1

h (1.5) = - 4.9 (1.5) ^2 + 14.7 (1.5) + 1

h (1.5) = 12.025 m