A plane is heading to a destination 1750 km due north at 175 km/h in a westward wind blowing 25 km/h. At what angle from north should the plane be oriented so that it reaches its destination?

dabuifs

123 To find the angle from the north at which the plane should be oriented, we can use trigonometry.

First, we need to find the resultant velocity of the plane. The westward wind affects the direction and speed of the plane.

Let's call the angle from the north at which the plane should be oriented as θ.

The component of the plane's velocity due north can be calculated as the plane's ground speed (175 km/h) times the cosine of θ:

Component north = 175 km/h * cos(θ)

The component of the plane's velocity due west can be calculated as the wind speed (25 km/h):

Component west = 25 km/h

The resultant velocity of the plane is the vector sum of these two components:

Resultant velocity = sqrt((Component north)^2 + (Component west)^2)

Since the plane is heading due north, the resultant velocity should also be pointing north. Therefore, the component west should be equal to zero, which gives us:

sqrt((Component north)^2 + (0)^2) = Component north

Simplifying the equation:

(175 km/h * cos(θ))^2 = (175 km/h)^2

175^2 * (cos(θ))^2 = 175^2

cos(θ)^2 = 1

cos(θ) = 1

θ = arccos(1)

θ = 0 degrees

So, the plane should be oriented at an angle of 0 degrees from the north. In other words, it should be pointed directly north to reach its destination.