A plane flies in a direction of N70°E for 80km ,then on a bearing of S10°W for 150km.
impatient much?
Once is enough, thank you.
Repeated postings will not get faster or better responses.
To solve this problem, we can break it down into two parts:
1. First, let's calculate the horizontal and vertical components of the plane's movement while flying N70°E for 80km.
The direction N70°E forms an angle of 70° with the reference North direction, and we can visualize it on a coordinate system.
- The horizontal component can be found using cosine:
horizontal component = 80 km * cos(70°) ≈ 33.49 km
- The vertical component can be found using sine:
vertical component = 80 km * sin(70°) ≈ 75.75 km
So, while flying N70°E for 80km, the plane covers approximately 33.49 km horizontally and 75.75 km vertically.
2. Next, let's calculate the horizontal and vertical components of the plane's movement while flying on a bearing of S10°W for 150km.
The direction S10°W forms an angle of 100° with the reference South direction.
- The horizontal component can be found using cosine:
horizontal component = 150 km * cos(100°) ≈ -59.14 km
- The vertical component can be found using sine:
vertical component = 150 km * sin(100°) ≈ -144.88 km
The negative sign indicates that the plane is going in the opposite direction of the reference South direction. So, while flying on a bearing of S10°W for 150km, the plane covers approximately -59.14 km horizontally and -144.88 km vertically (opposite to the South direction).
To find the total displacement, we can add up the horizontal and vertical components:
Total horizontal displacement = 33.49 km + (-59.14 km) = -25.65 km (approximately)
Total vertical displacement = 75.75 km + (-144.88 km) = -69.13 km (approximately)
The negative sign indicates that the displacement is in the opposite direction of our reference point.
Therefore, the plane's total displacement is approximately 25.65 km towards the West and 69.13 km opposite to the South direction.
To represent the flight path of the plane, we can use a diagram with an arrow depicting the distances and directions traveled.
1. Start by drawing a line to represent the starting point of the plane.
2. From the starting point, draw an arrow pointing to the northeast direction (N70°E). Label this arrow as "80 km."
80 km ------> (N70°E)
3. Next, at the end point of the first arrow, draw another arrow pointing to the southwest direction (S10°W). Label this arrow as "150 km."
(N70°E)
80 km ---------->
150 km ---------> (S10°W)
This diagram shows the flight path of the plane traveling N70°E for 80 km and then S10°W for 150 km.