Answer:
The time taken for the flare to hit the ground is approximately 10.7 seconds.
Step-by-step explanation:
Given : Suppose a flare is shot from the top of a 120 foot building at a speed of 160 feet per second. The equation [tex]h =- 16t^2+ 160t + 120[/tex] models the h height at t seconds of the flare.
To find : How long will it take for the flare to hit the ground?
Solution :
The equation [tex]h =- 16t^2+ 160t + 120[/tex] models the h height at t seconds of the flare.
The flare to hit the ground when h=0.
Substitute in the equation,
[tex]-16t^2+ 160t + 120=0[/tex]
Applying quadratic formula, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Where, a=-16, b=160 and c=120
[tex]x=\frac{-160\pm\sqrt{160^2-4(-16)(120)}}{2(-16)}[/tex]
[tex]x=\frac{-160\pm\sqrt{33280}}{-32}[/tex]
[tex]x=\frac{-160\pm 182.42}{-32}[/tex]
[tex]x=\frac{-160+182.42}{-32},\frac{-160-182.42}{-32}[/tex]
[tex]x=−0.70,10.70[/tex]
Reject the negative value.
Therefore, the time taken for the flare to hit the ground is approximately 10.7 seconds.
