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 been?
$$\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right. \text { ) }$$
A) $8

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 been?
$$\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right. \text { ) }$$
A) $8 < t < 11$
B) $0 < t < 4$
C) $4 < \mathrm { t } < 7$
D) $12 < \mathrm { t } < 15$

Quizplus · Accepted Answer

The equation for the height of the flare is given by $h = -16t^2 + v_0t + h_0$, where $v_0 = 176 \, \text{ft/sec}$ (initial velocity) and $h_0 = -448 \, \text{ft}$ (initial height, since the gorge is 448 ft deep, we consider it as negative). To find when the flare is above the rim (i.e., when $h > 0$), we set $h = 0$ and solve for $t$:$$0 = -16t^2 + 176t - 448$$Dividing the entire equation by -16 to simplify, we get:$$t^2 - 11t + 28 = 0$$Factoring the quadratic equation, we find:$$(t - 4)(t - 7) = 0$$Thus, $t = 4$ and $t = 7$. This means the flare is above the rim of the gorge between $t = 4$ seconds and $t = 7$ seconds.

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

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