From the given question, we can deduce the following information:
• Time, t = 4 hours
,
• The hiker goes from 892 ft to 256 ft above the canyon floor.
Let's find the vertical speed of the hiker.
To find the speed, apply the formula:
![speed=(dis\tan ce)/(time)](https://img.qammunity.org/2023/formulas/mathematics/college/53vojwjkpxe1ozjo38aa0lzoxomwd4krr3.png)
To find the distance, we have:
Distance covered = 256 ft - 892 ft = -636 ft.
Hence, to find the vertical speed, we have:
![\begin{gathered} speed=(dis\tan ce)/(time) \\ \\ \text{speed}=(-636)/(4)=-159\text{ ft/h} \\ \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/1arp0uroc96qfidxwbokadd7l8vob93d07.png)
Therefore, the vertical speed of the hiker is -159 feet per hour.
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