Answer: it will take 8.25 seconds to reach maximum height
Explanation:
Initial velocity, u of baseball = 132 feet per second. The height of the baseball, h in feet after t seconds is given by the function h = −16t^2 + 132t + 4
The given function is a quadratic equation. If values of height attained is plotted against time, the graph will take the shape of a parabola whose vertex corresponds to the maximum height attained by the baseball
Vertex of the parabola = -b/2a
a = - 16
b = 132
Vertex = - 132/-16× 2 = -132/32
Vertex = 4.125
The maximum height is 4.125 feets
To determine the time it will take to reach the maximum height of 4.125 feets, we will substitute h = 4.125 in the equation
4.125 = −16t^2 + 132t + 4
−16t^2 + 132t - 0.125 = 0
Applying the general formula for quadratic equations,
t = [- b ± √b^2 - (4ac)]/2a
a = -16
b = 132
c = -0.125
t = [- 132 ± √132^2 - 4(-16 × - 0.125)]/2× -16
t = [- 132 ± √17424 - 8)]/-32
t = [- 132 ± √17416]/-32
t = (-132 ± 132)/-32
t = (-132 + 132)/-32 or (-132 -132)/-32
t = 0 or -264/-32
t = 8.25 seconds