A plane's flight path called for it to fly from J to W. W is 200kms due North and 500kms due west of J. Draw a coordinate picture. What bearing will the pilot fly and what distance will he or she go in air kilometers?
First step. Draw the picture.
Do you know the Pythagorean Theorem?
Can you convert from x-y to headings?
Length of side answered. Can not find bearing of angle .4
if you set J at (0,0), then W is at (-500,200).
Check your formulas, and you will find that the plane's heading (not bearing!) is
360-arctan(200/500)
359.6
To solve this question, we can draw a coordinate picture and use trigonometry to find the bearing and distance of the flight path.
1. Draw a coordinate system with a point labeled "J" as the origin (0,0).
2. Place point "W" 500kms west and 200kms north of point J. The coordinates of W will be (-500, 200).
- Keep in mind that positive x-values represent eastward direction, and positive y-values represent northward direction.
Now, let's calculate the bearing and distance:
1. Calculate the bearing:
- The bearing is the angle measured clockwise from the north direction.
- We can use the arctan (inverse tangent) function to find the angle.
- Calculate the angle using the coordinates of W relative to J:
Bearing (θ) = arctan((y-coordinate of W) / (x-coordinate of W))
= arctan(200 / -500)
≈ -21.8 degrees (rounded to one decimal place)
- Since we are measuring the angle clockwise from the north, the bearing is 360 degrees - 21.8 degrees ≈ 338.2 degrees (rounded to one decimal place).
- Therefore, the pilot will fly on a bearing of approximately 338.2 degrees.
2. Calculate the distance in air kilometers:
- We can use the Pythagorean theorem to find the length of the flight path.
- The length of the flight path is the hypotenuse of a right triangle formed by the coordinates of J and W.
- Calculate the distance using the coordinates of W relative to J:
Distance = √((x-coordinate of W)^2 + (y-coordinate of W)^2)
= √((-500)^2 + 200^2)
= √(250,000 + 40,000)
= √290,000
≈ 538.5 kms (rounded to one decimal place).
Therefore, the pilot will fly on a bearing of approximately 338.2 degrees, and the distance of the flight path will be approximately 538.5 kilometers.