Solve the problem.
-A flare is fired from the bottom of a gorge with an initial velocity of 80 feet per second, and it is visible only when the flare is above the rim. The height of the flare, in feet, after t seconds is given
By the function h(t) = -16t2 + 80t. If the gorge is 96 feet deep, for what length of time can the flare
Be seen?
A) 0 sec to 2 sec
B) 4 sec to 5 sec
C) 6 sec to 7 sec
D) 2 sec to 3 sec

Question

Quizplus · Accepted Answer

To find when the flare can be seen, we need to determine when its height is above 96 feet. The equation for the height of the flare is $h(t) = -16t^2 + 80t$. To find when the flare is above the rim of the gorge (96 feet), we set $h(t) = 96$ and solve for $t$:$$-16t^2 + 80t = 96$$Rearrange the equation:$$-16t^2 + 80t - 96 = 0$$Divide the entire equation by -16 to simplify:$$t^2 - 5t + 6 = 0$$Factoring the quadratic equation gives:$$(t - 2)(t - 3) = 0$$So, $t = 2$ or $t = 3$.This means the flare is above 96 feet between 2 seconds and 3 seconds after it is fired.

Solve the Problem. -A Flare Is Fired from the Bottom of a Gorge