Question

Betty is ziplining and drops 8 meters in elevation for every 40 meters he travels horizontally. If he starts at 1900 meters and travels at 20 meters per second, what is his elevation, in meters, at time t?

Answer 1

Betty's elevation at time t while ziplining can be calculated by subtracting the elevation drop, which is 4t meters, from her initial elevation of 1900 meters. Hence, her elevation at time t is 1900 - 4t meters.

Step-by-step explanation:

To solve for Betty's elevation at time t while ziplining, we must use the given ratios and her initial elevation. Betty drops 8 meters in elevation for every 40 meters she travels horizontally. If she travels at 20 meters per second, we can find out how far she travels horizontally at any time t and then calculate the corresponding change in elevation.

The horizontal distance traveled at time t is given by the equation distance = speed × time, or d = 20 meters/second × t. For every 40 meters of horizontal travel, the elevation drops by 8 meters, so the drop in elevation at time t is (d/40) × 8. Substituting d with 20t gives us the elevation drop of t: (20t/40) × 8 = 4t.

To find Betty's elevation at time t, we subtract the elevation drop from her initial elevation of 1900 meters: Elevation at time t = initial elevation - elevation drop = 1900 - 4t.