A rock is tossed upward. Its height after t seconds is given by S = - 16t2 + 24t + 3 feet. What is its maximum height? When does it reach that height?

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