Question

Which function could represent the height in feet, h, of a soccer ball t seconds after being kicked from an initial height of 1 foot?

Answer 1

Let h is the height of the ball after t seconds

The acceleration upward = -32 feet/sec.^2

This situation must be represented by a quadratic function

The form of the function is:

`h=ut+(1)/(2)at^2+h_0`

u is the initial velocity

a is the acceleration of gravity

t is the time

h0 is the initial height

From the given, the initial height is 1 foot

The acceleration of gravity is a constant value -32 ft/s^2

The initial velocity is unknown

Let us substitute the values given in the function

`\begin{gathered} h=ut+(1)/(2)(-32)t^2+1 \\ h=ut-16t^2+1 \end{gathered}`

Let us arrange the terms from greatest power of t

`h=-16t^2+ut+1`

We have only 1 function in the choices similar to our function

`h=-16t^2+25t+1`

The answer is the second choice