Question

Ariana has created a paper airplane for her physics class, the physics teacher is requiring her paper airplane to swoop down at a single point to graze the ground before it rises back into the air. Her initial attempt is modeled by the function below where h is height in feet and X is time in seconds. In how many seconds will the paper airplane crash into the ground?

Answer 1

Given:

`h(x)=x^2-12x+35`

The given function h(x) represents the height in feet and (x) is time in seconds.

We will find the time the paper airplane will crash into the ground.

When the paper airplane crashes into the ground, h(x) = 0

So, substitute h = 0

`x^2-12x+35=0`

Solve the equation to find (x), we will factor the equation as follows:

`\begin{gathered} (x-5)(x-7)=0 \\ x-5=0\rightarrow x=5 \\ x-7=0\rightarrow x=7 \end{gathered}`

So, the answer will be the time = 5 seconds and 7 seconds