Question

juanita is testing her new model airplane. she starts its descent at an elevation of 2,500 feet. it descends at a constant rate of 500 feet per minute. we can extend the graph to see when the plane lands. how many minutes after the start of its descent does the plane land? the plane lands minutes after it starts to descend.

Explanation:

Step1: Identify the problem type

This is a linear relationship problem where elevation (e) decreases over time (t) at a constant rate. The initial elevation is 2500 feet, and the rate of descent is 500 feet per minute. We need to find the time when elevation e = 0 (plane lands).

Step2: Set up the equation

The elevation as a function of time can be modeled by the linear equation \( e = 2500 - 500t \), where \( e \) is elevation in feet and \( t \) is time in minutes. We want to find \( t \) when \( e = 0 \).

Step3: Solve for t

Set \( e = 0 \) in the equation:

$$ 0 = 2500 - 500t $$

Add \( 500t \) to both sides:

$$ 500t = 2500 $$

Divide both sides by 500:

$$ t = \frac{2500}{500} = 5 $$

Alternatively, from the graph, we can see that the line intersects the t - axis (where e = 0) at t = 5 minutes.

Answer:

5