Question

During an airplanes ascent, the plane reaches a horizontal distance from the airport of 1 km and then 7 km. The plane ascends at a slope of 2/3. Find the vertical distance (y) in feet that the plane traveled during the indicated spots

Answer 1

The vertical distance in feet that the plane traveled was 4 Km

Explanation:

The Slope of a Line

Suppose we know a line passes across points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

The airplane ascent will be modeled with the equation of a line because we are given a constant slope of m=2/3. We also know the horizontal distances are x1=1 Km and x2=7 Km. Substituting in the formula above:

`\displaystyle (2)/(3)=(y_2-y_1)/(7-1)`

Operating:

`\displaystyle (2)/(3)=(y_2-y_1)/(6)`

Solving for y2-y1, we get the vertical distance traveled by the plane:

`\displaystyle y_2-y_1=6*(2)/(3)=4`

Thus, the vertical distance in feet that the plane traveled was 4 Km