Question

Sarah kicked a ball in the air. The function

Answer 1

Answer: The ball hits the ground at 5 s

Step-by-step explanation:

The question seems incomplete and there is not enough data. However, we can work with the following function to understand this problem:

$f=30 t- 6t^{2}$ (1)

Where $f$ models the height of the ball in meters and $t$ the time.

Now, let's find the time $t$ when the ball Sara kicked hits the ground (this is when $f=0 m$):

$0=30 t- 6t^{2}$ (2)

Rearranging the equation:

$6t^{2}-30 t=0$ (3)

Dividing both sides of the equation by $6$:

$t^{2}-5 t=0$ (4)

This quadratic equation can be written in the form $at^{2}+bt+c=0$, and can be solved with the following formula:  

$t=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$ (5)  

Where:  

$a=1$  

$b=-5$  

$c=0$  

Substituting the known values:  

$t=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(0)}}{2(1)}$ (6)  

Solving we have the following result:

$t=5 s$  This means the ball hit the ground 5 seconds after it was kicked by Sara.