QuestionFind the horizontal distance the jet flies to reach $12,000$ ft altitude with a slope of $m=3/8$ .

Studdy Solution

STEP 1

Assumptions1. The slope of the airplane's climb is $m=3/8$ . . The airplane needs to reach an altitude of $12,000$ ft.
3. The slope is the ratio of the vertical distance (altitude) to the horizontal distance (distance flown).
4. The airplane's climb is a straight line from the takeoff point to the point at $12,000$ ft altitude.

STEP 2

The slope of the airplane's climb is defined as the ratio of the vertical distance to the horizontal distance. We can express this as $m = \frac{vertical\,distance}{horizontal\,distance}$

STEP 3

We know the slope $m$ and the vertical distance (altitude), so we can solve for the horizontal distance. Rearrange the equation to solve for the horizontal distance $horizontal\,distance = \frac{vertical\,distance}{m}$

STEP 4

Plug in the given values for the vertical distance (altitude) and slope $m$ to calculate the horizontal distance.
$horizontal\,distance = \frac{12,000\,ft}{3/8}$

STEP 5

Calculate the horizontal distance.
$horizontal\,distance = \frac{12,000\,ft}{3/8} =32,000\,ft$ The airplane will fly $32,000$ feet in the horizontal direction to reach an altitude of $12,000$ feet above the takeoff point.

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