A hiker descends a steep mountain with a constant speed. If the incline is 30 degrees, and it takes the hiker 20 minutes to descend 1 kilometer, calculate the hiker's speed and the vertical descent.
Guide On Rating System
Vote
To calculate the hiker's speed, we need to convert the 20 minutes into hours. There are 60 minutes in an hour, so 20 minutes is 20/60 = 1/3 of an hour.
Since the hiker descends 1 kilometer in 1/3 of an hour, their speed is 1 kilometer / (1/3 hour) = <<1/(1/3)=3>>3 kilometers per hour.
The incline of the mountain is 30 degrees. The vertical descent is the component of the distance traveled that is in the downward direction. We can calculate this using trigonometry.
The vertical descent is given by the formula:
Vertical descent = Distance * sin(angle)
The distance traveled is 1 kilometer, so the vertical descent is 1 * sin(30) = 1 * 0.5 = 0.5 kilometers.
Therefore, the hiker's speed is 3 kilometers per hour, and the vertical descent is 0.5 kilometers.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99