A line directed to the west. A plane flies 20 degrees north of that direction ( 90 degrees north of that direction would be north..) if the plane flies for 340 km, determine its displacement toward the west and its displacement toward the north during its flight?
West = 340*Cos20 = 319.5 km.
North = 340*sin20 = 116.3 km.
To determine the displacement of the plane towards the west and north, we can use trigonometry. Let's break down the problem step by step:
1. Draw a diagram: Draw a line directed to the west (←). Mark a point on this line to represent the starting position of the plane.
2. Determine the angle: The plane flies 20 degrees north of the west direction. Since 90 degrees north of the west direction would be north, the plane is flying 20° north of west.
3. Calculate the northward displacement: To calculate the displacement towards the north, we can use the sine function. The formula is: displacement north = distance * sin(angle).
In this case, the angle is 20 degrees and the distance is 340 km. Using the formula:
displacement north = 340 km * sin(20°) ≈ 115.98 km.
Therefore, the plane's displacement towards the north during its flight is approximately 115.98 km.
4. Calculate the westward displacement: To calculate the displacement towards the west, we can use the cosine function. The formula is: displacement west = distance * cos(angle).
Using the same values as before, we have:
displacement west = 340 km * cos(20°) ≈ 313.51 km.
Therefore, the plane's displacement towards the west during its flight is approximately 313.51 km.
To summarize:
- Displacement toward the north = 115.98 km
- Displacement toward the west = 313.51 km.