A pilot of a single engine airplane flies at a constant speed of 200 km/h at a bearing of 25 degree north east there is 40 km/h crosswind blowing south east 45 degree what are plane's actual speed and direction ?
Answer me
iuy
To find the actual speed and direction of the plane, we need to calculate the components of the velocity vector caused by the wind and the actual velocity of the plane.
Let's break down the velocity of the plane into two components:
1. Component in the north-south direction: This component is given by the formula: Actual speed x sin(direction angle).
2. Component in the east-west direction: This component is given by the formula: Actual speed x cos(direction angle).
Given:
- Speed of the plane = 200 km/h
- Bearing (direction angle) = 25 degrees northeast
- Crosswind speed = 40 km/h
- Crosswind direction = southeast at a 45-degree angle
Now, let's calculate the wind's components in the north-south and east-west directions:
- Wind's north-south component = Crosswind speed x sin(crosswind direction angle)
- Wind's east-west component = Crosswind speed x cos(crosswind direction angle)
Using the given information:
- Wind's north-south component = 40 km/h x sin(45 degrees) = 28.28 km/h southward
- Wind's east-west component = 40 km/h x cos(45 degrees) = 28.28 km/h eastward
Now, we can add the components of the plane's velocity and wind's velocity to get the actual speed and direction of the plane.
- Actual speed of the plane = Speed of the plane - Wind's east-west component = 200 km/h - 28.28 km/h = 171.72 km/h
- Actual direction of the plane = Bearing (direction angle) + inverse tangent (Wind's north-south component / Wind's east-west component)
= 25 degrees + inverse tangent (28.28 km/h / 28.28 km/h) = 25 degrees
Therefore, the plane's actual speed is 171.72 km/h, and its actual direction is 25 degrees northeast.