Answer:
Step-by-step explanation:
The height of the rock ,(s), in feets after t seconds is given by the function
S = −16t^2 + 24t + 3
The given function is a quadratic equation. If values of height attained is plotted against time, the shape of the graph will be a parabola whose vertex would correspond to the maximum height obtained by the object.
Vertex of the parabola = -b/2a
a = - 16
b = 24
Vertex = - 24/- 16×2 = 24/32
Vertex = 0.75
So the maximum height is 0.75 feet
To determine the time at which it will reach a maximum height of 0.75, we will substitute s = 0.75 into the equation.
S = −16t^2 + 24t + 3
0.75 = −16t^2 + 24t + 3
−16t^2 + 24t + 2.25 = 0
Applying the general formula for quadratic equation,
t = b ± √b^2 - (4ac)]/2a
a = -16
b = 24
c = 2.25
t = - 24 ± √24^2 - 4(-16 × 2.25)]/2×-16
t = - 24 ± √(576 + 144)]/-32
t = - 24 ± √(720)/-32
t = (- 24 ± 26.83)/-32
t = 2.83/-32 or t = -50.83 /-32
t = - 0.088 or t = 1.588
The time cannot be negative so,
The time take to reach maximum height is 1.588 seconds
