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?
$$\text { (h } \left. = - 16 \mathrm { t } ^ { 2 } + \mathrm { v } _ { \mathrm { O } } \mathrm { t } + \mathrm { h } _ { \mathrm { O } } \right)$$
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?
$$\text { (h } \left. = - 16 \mathrm { t } ^ { 2 } + \mathrm { v } _ { \mathrm { O } } \mathrm { t } + \mathrm { h } _ { \mathrm { O } } \right)$$
A) $15 < t < 17$
B) $10 < \mathrm { t } < 12$
C) $5 < \mathrm { t } < 7$
D) $0 < t < 5$

Quizplus · Accepted Answer

The equation of motion is $h = -16t^2 + 192t + 560$, where $h$ is the height above the bottom of the gorge, $t$ is the time in seconds, $v_0 = 192 \mathrm { ft } / \mathrm { sec }$ is the initial velocity, and $h_0 = 560 \mathrm { ft }$ is the initial height (depth of the gorge). To find when the flare is visible above the rim, set $h = 0$ and solve for $t$. This gives the times when the flare is at the level of the rim, marking the start and end of visibility. Solving $0 = -16t^2 + 192t + 560$ yields $t$ values that indicate the flare is visible between approximately 5 and 7 seconds.

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

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