You wonder what altitude the plane reached when it was directly above the end of the runway and how far it travelled to get to that point.
You know the runway tarmac is 5500 metres long and approximate that when the plane left the ground, it took off at an angle of 40 degrees. The plane travelled along the runway for about 5000 metres.
What is the plane’s height vertically when it is directly above the end of the runway? How far did the plane travel to get to the point directly above the end of the runway?
you don't approximate, you estimate.
so, the plane was off the ground for the last 500 meters. At that point, it was at a height h, where
h/500 = tan40°
The plane's ascending distance d is
500/d = cos40°
When the plane is directly above the runway, it is at an altitude of 652.7m
To find the plane's height vertically when it is directly above the end of the runway, we can use trigonometry. Let's break down the problem step by step:
1. Draw a diagram: Start by drawing a diagram that represents the given scenario. Label the runway length (5500m), the angle of takeoff (40 degrees), and the distance traveled along the runway (5000m).
2. Find the vertical height: Using trigonometry (specifically, the sine function), we can find the vertical height. The formula for finding the height (h) is: h = distance traveled along the runway x sin(angle of takeoff). Plug in the values we know: h = 5000m x sin(40 degrees).
3. Calculate the height: Use a calculator to find the sine of 40 degrees and multiply it by 5000m to get the vertical height. The result will be the height above the end of the runway.
4. Find the distance traveled horizontally: To find the distance the plane traveled to get to the point directly above the end of the runway, we can use the cosine function. The formula for finding the distance (d) is: d = distance traveled along the runway x cos(angle of takeoff). Plug in the values we know: d = 5000m x cos(40 degrees).
5. Calculate the distance: Use a calculator to find the cosine of 40 degrees and multiply it by 5000m to get the horizontal distance. The result will be the distance traveled to get to the point directly above the end of the runway.
By following these steps, you will be able to find the plane's height vertically when it is directly above the end of the runway and the distance it traveled to get to that point.