A plane flys 230 km due north. The wind is blowing west at 85 km. what direction is the plane flying. Calculate the actual speed of the plane. What is the hearing from North?
When you say " The wind is blowing west ", I will assume "from" the usual west.
Your vector diagram would result in a right-angled triangle.
Let the actual speed of the plane be r
r^2 = 230^2+85^2
= ...
r = √...
let the angle be Ø
sinØ = 85/r
Ø = ...
direction:
N Ø E
To determine the direction in which the plane is flying, we need to consider the direction of the wind and the direction of the plane's trajectory.
The plane is flying due north, which means it is heading directly towards the north. The wind, on the other hand, is blowing west.
Since the wind is blowing perpendicular to the direction of the plane's travel, it will not affect the direction in which the plane is flying. Therefore, the plane is still flying due north.
To calculate the actual speed of the plane, we need to use vector addition. We can treat the plane's distance traveled as a vector pointing north and the wind's speed as a vector pointing west.
Using the Pythagorean theorem, we can determine the actual speed of the plane:
Actual speed = √(plane's speed)^2 + (wind's speed)^2
= √(230)^2 + (85)^2
= √(52900 + 7225)
= √(60125)
≈ 245.04 km/h
To find the bearing from the North, we need to use trigonometry. Since the plane is heading due north, the bearing can be calculated as the angle formed between the line connecting north to the plane and the line connecting north to a reference direction (such as east or west).
In this case, we'll calculate the bearing from the north to the west. We can use the inverse tangent function (tan⁻¹) to find the angle:
Bearing from North = tan⁻¹(wind's speed / plane's speed)
= tan⁻¹(85 / 230)
̴ tan⁻¹(0.3696)
≈ 21.03°
Therefore, the plane is flying due north with an actual speed of approximately 245.04 km/h, and the bearing from the north to the west is approximately 21.03°.