Answer:
The correct option is b: 6 seconds.
Step-by-step explanation:
The formula is:
[tex] h = -16t^{2} + 32t + 384 [/tex]
Where:
t: is the time
h: is the height = 384 ft
When the stone hit the ground, h = 0
[tex] 0 = -16t^{2} + 32t + 384 [/tex]
To solve the above quadratic equation we need to use the following formula:
[tex]t = \frac{-b \pm \sqrt{b^{2} -4ac}}{2a}[/tex] (1)
Where:
a: is the coefficient of t² = -16
b: is the coefficient of t = 32
c: is the independent term = 384
By entering the above values into equation (1) we have:
[tex]t = \frac{-32 \pm \sqrt{32^{2} -4(-16)(384)}}{2(-16)} = \frac{-32 \pm \sqrt{25600}}{-32} = \frac{-32 \pm 160}{-32}[/tex]
[tex] t_{1} = \frac{32+160}{32} = 6 [/tex]
[tex] t_{2} = \frac{32-160}{32} = -4 [/tex]
Since we can not take the negative value of time (t₂) equal to -4, the answer is 6 seconds.
Therefore, the stone will hit the ground in 6 seconds. The correct option is b: 6 seconds.
I hope it helps you!
