A plane flies due west at 250 km/hour while the wind blows south at 70 km/hour. Find the planes resultant velocity and direction.
To find the resultant velocity of the plane, we need to consider the velocities of both the plane and the wind. We can use vector addition to find the resultant velocity.
Let's break down the velocities into their components:
The velocity of the plane flying due west at 250 km/hour can be represented as (-250, 0), where the x-component is -250 km/hour and the y-component is 0 km/hour.
The velocity of the wind blowing south at 70 km/hour can be represented as (0, -70), where the x-component is 0 km/hour and the y-component is -70 km/hour.
To find the resultant velocity, we can add the corresponding components of the plane's and the wind's velocities. In this case, the x-component will be (-250 + 0) = -250 km/hour, and the y-component will be (0 - 70) = -70 km/hour.
So, the resultant velocity of the plane is (-250, -70), which means the plane is moving at a speed of 250 km/hour in the west direction and 70 km/hour in the south direction.
To find the magnitude of the resultant velocity, we can use the Pythagorean theorem:
Resultant velocity = √((-250)^2 + (-70)^2) ≈ 261.71 km/hour
To find the direction of the resultant velocity, we can use inverse tangent (tan⁻¹) function:
θ = tan⁻¹(-70 / -250) ≈ 16.26° (measured counterclockwise from the positive x-axis)
So, the plane's resultant velocity is approximately 261.71 km/hour in the direction of 16.26° east of south.