If a runner is running uphill at an
angle of at 8 miles per hour, what
is her speed in the vertical direction?
(Round her speed to the nearest
tenth.)

To find the vertical component of the runner’s speed, we can use the sine function, which gives us the opposite side of a right triangle when we know the hypotenuse and the angle. The vertical speed (V_vertical) can be calculated as:

Where mph and . Plugging in the values:

So rounded to the nearest tenth, the runner’s speed in the vertical direction is 4.0 miles per hour.

But what’s the significance of this calculation in the broader world of running? Many runners might not realize how incline affects their performance. Uphill running increases the workload significantly, with more energy exerted during the stride. By calculating vertical speed, athletes can better monitor their training intensity and make adjustments as needed for building strength and endurance!