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 4.9 t squared plus 34.3 t plus 1h(t)=â4.9t2+34.3t+1. how long does it take for the baseball to reach its maximumâ height? what is the maximum height obtained by theâ baseball?

The height at time t is given by
h(t) = -4.91t² + 34.3t + 1

When the ball reaches maximum height, its derivative, h'(t) = 0.
That is,
-2(4.91)t+34.3 = 0
-9.82t + 34.3 = 0
t = 3.4929 s

Note that h''(t) = -9.82 (negative) which confirms that h will be maximum.

The maximum height is
hmax = -4.91(3.4929)² + 34.3(3.4929) + 1
          = 60.903 m

The ball attains maximum height in 3.5 s (nearest tenth).
The ball attains a maximum height of 60.9 m (nearest tenth)