Question

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?

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