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 $192 \mathrm { ft } / \mathrm { sec }$, and the gorge is $560 \mathrm { ft }$ deep, during what interval can the flare be seen?
$$\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right. \text { ) }$$
A) $15

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 $192 \mathrm { ft } / \mathrm { sec }$, and the gorge is $560 \mathrm { ft }$ deep, during what interval can the flare be seen?
$$\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right. \text { ) }$$
A) $15 < t < 17$
B) $10 < \mathrm { t } < 12$
C) $5 < t < 7$
D) $0 < t < 5$

Quizplus · Accepted Answer

The equation for the height $h$ of the flare at time $t$ seconds is given by $h = -16t^2 + 192t + 0$, since the initial height $h_0$ is 0 (fired from the bottom) and the initial velocity $v_0$ is $192 \mathrm { ft } / \mathrm { sec }$. The flare is visible only when it is above the rim of the gorge, which means $h > 560$. To find when the flare is above 560 ft, we solve the inequality:$$ -16t^2 + 192t > 560 $$$$ -16t^2 + 192t - 560 > 0 $$$$ t^2 - 12t + 35 < 0 $$$$ (t - 5)(t - 7) < 0 $$This inequality is true between the roots, so $5 < t < 7$.

Solve the Problem 192ft/sec192 \mathrm { ft } / \mathrm { sec }192ft/sec

Solve the Problem $192 \mathrm { ft } / \mathrm { sec }$