Answer:
Option 3.
Step-by-step explanation:
The given function is
[tex]h(t)=-16t^2-30t+124[/tex]
where, h(t) is the height of a small rock falling from the top of a 124-ft-tall building and t is the time in seconds.
It is a downward parabola.
Equate the function equal to 0, to find the time at which the rock touch the ground.
[tex]-16t^2-30t+124=0[/tex]
If [tex]ax^2+bx+c=0[/tex], the according to the quadratic formula
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Using quadratic formula, we get
[tex]t=\dfrac{-(-30)\pm \sqrt{(-30)^2-4(124)(-16)}}{2(-16)}[/tex]
[tex]t=\dfrac{30+\sqrt{(-30)^2-4(124)(-16)}}{2(-16)},\dfrac{30-\sqrt{(-30)^2-4(124)(-16)}}{2(-16)}[/tex]
[tex]t=-3.875, 2[/tex]
Time cannot be negative. So, the rock remain in the air in the interval 0 < t < 2.
Therefore, the correct option is 3.
