Question

A baseball player swings and hits a pop fly straight up in air to the catcher. the height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t)=-4.9t^(2)+34.3t+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

$h(t)=-4.9t^{2}+34.3t+1 \\h'(t)=(-4.9t^{2}+34.3t+1)'=-9.8t+34.3 \\h'(t)=0 \\-9.8t+34.3=0 \\ \\t= \frac{34.3}{9.8} =3.5 \\ \\h_{max}=h(3.5)=-4.9\times3.5^{2}+34.3\times3.5+1=61.025$

The ball reaches its maximum height after 3.5 seconds, and the maximum height is 61.025 meters.