an airplane's altitude is 100 feet as it descents for a landing on a runway whose touchdown is 5000 ft away. Let the x-axis represent the ground and the y-axis represent the airplane's altitude. What is the slope of the airplane's descent? What is the y-intercept of the airplane's descent? Write a model of the plane's flight.
You’re piloting an airplane. To prepare for landing, you change the plane’s altitude from a meters to c meters.
To find the slope of the airplane's descent, we need to determine the change in altitude (y-axis) for every unit change in distance (x-axis).
Given:
Initial altitude = 100 feet
Touchdown point distance = 5000 ft
Change in altitude = 100 - 0 (since the plane starts at an altitude of 100 feet)
Change in distance = 5000 - 0
Slope = Change in altitude / Change in distance
Slope = (100 - 0) / (5000 - 0)
Slope = 100 / 5000
Slope = 0.02
Therefore, the slope of the airplane's descent is 0.02.
To determine the y-intercept of the airplane's descent, we need to find the altitude when the distance is zero (x = 0). We know that the y-intercept is the point where the line intersects the y-axis.
Given:
Initial altitude = 100 feet
The y-intercept is the altitude at x = 0, which is 100 feet.
Therefore, the y-intercept of the airplane's descent is 100 feet.
To write a model of the plane's flight, we can use the slope-intercept form of a linear equation, which is y = mx + b (where m is the slope and b is the y-intercept).
Therefore, the model of the plane's flight is:
y = 0.02x + 100
To find the slope of the airplane's descent, we need to calculate its rate of vertical change with respect to horizontal distance.
The airplane's altitude decreases by 100 feet as it covers a horizontal distance of 5000 feet. So, the slope can be calculated as:
Slope = vertical change / horizontal change
= -100 ft / 5000 ft
= -0.02
Therefore, the slope of the airplane's descent is -0.02.
To find the y-intercept of the airplane's descent, we need to determine the point where the airplane crosses the y-axis (when it is 0 feet above the ground).
Given that the starting altitude of the airplane is 100 feet, we can conclude that the y-intercept of the descent is (0, 100).
Now, let's write the model of the plane's flight using the slope-intercept form of a linear equation, y = mx + b, where y represents the airplane's altitude and x represents the horizontal distance.
The equation will be: y = -0.02x + 100
This equation represents the relationship between the airplane's altitude and the distance it has traveled. As the airplane moves closer to the touchdown point, its altitude decreases by 0.02 feet for every foot of horizontal distance traveled.
During the descent,
the change in y is -100
the change in x is 5000
so, the slope is -100/5000 = -1/50 = -0.02
The y-intercept is when x=0. That is, at the start of the landing. y=100.
so, y = -0.02x + 100