Solve the problem.
-A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of $176 \mathrm { ft } / \mathrm { sec }$, and the gorge is $448 \mathrm { ft }$ deep, during what interval can the flare be seen? $\left( h = - 16 t ^ { 2 } + v _ { O } t + \right.$ $\left. \mathrm { h } _ { \mathrm { O } } \right)$
A) $0

Question

Solve the problem.
-A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of $176 \mathrm { ft } / \mathrm { sec }$, and the gorge is $448 \mathrm { ft }$ deep, during what interval can the flare be seen? $\left( h = - 16 t ^ { 2 } + v _ { O } t + \right.$ $\left. \mathrm { h } _ { \mathrm { O } } \right)$
A) $0 < t < 4$
B) $8 < t < 11$
C) $4 < \mathrm { t } < 7$
D) $12 < t < 15$

Quizplus · Accepted Answer

The flare is visible when its height $ h $ is greater than 0. Solving the equation $ -16t^2 + 176t - 448 = 0 $ gives the times when the flare is at the rim. Solving this quadratic equation gives $ t = 4 $ and $ t = 7 $. Thus, the flare is visible between $ t = 4 $ and $ t = 7 $.

Solve the Problem 176ft/sec176 \mathrm { ft } / \mathrm { sec }176ft/sec

Solve the Problem $176 \mathrm { ft } / \mathrm { sec }$