Question

April shoots an arrow upward into the air at a speed of 64feet per second from a platform that is 28feet high. The height of the arrow is given by the function h(t)= -16t^2+64t+28, where t is the time in seconds. what is the maximum height of the arrow?

Answer 1

92 feet

Step-by-step explanation:

Given the speed of the arrow as 64 feet per second and the height of the platform as 28 feet.

Given the below function;

`h(t)=-16t^2+64t+28`

The above is given in the form of a quadratic function;

`f(x)=ax^2+bx+c`

If we compare both functions, we can see that a = -16, b = 64 and c = 28.

Since the motion of the arrow is modeled by a quadratic function, it means that it will take the shape of a parabola.

The x-coordinate of the maximum point(vertex) of a parabola is generally determined by the below formula;

`x=(-b)/(2a)`

Let's go ahead and determine t at maximum point by substituting the above values into our vertex formula;

`t=(-64)/(2(-16))=(-64)/(-32)=2`

To determine the maximum height, all we need to do is substitute t = 2 into the given equation of a parabola and solve for h;

`\begin{gathered} h(2)=-16(2)^2+64(2)+28 \\ =-64+128+28 \\ =92ft \end{gathered}`

We can see from the above that the maximum height of the arrow will be 92ft