Question

A. What is the resultant speed of the airplane when the pilot points the airplane due South with an airspeed of 120 miles per sec while a steady wind blows due West at 40 miles per sec?

b. What is the angle (direction, θ) of the plane referenced above?

Answer 1

The resultant speed of the airplane when pointing due South with an airspeed of 120 miles per second and a steady west wind of 40 miles per second is 160 miles per second. The angle (direction) of the plane is 90° south of west.

Step-by-step explanation:

To find the resultant speed of the airplane, we need to consider the velocities of the airplane and the wind separately and add them up. Given that the airspeed of the airplane is 120 miles per second to the South and the wind blows due West at 40 miles per second, we can use vector addition to find the resultant speed.

First, let's break down the velocities into their North and West components. The airspeed of the airplane has a North component of 0 miles per second and a West component of -120 miles per second. The wind has a North component of 0 miles per second and a West component of -40 miles per second.

Next, we add up the North and West components separately. The North component is 0 miles per second + 0 miles per second, which is 0 miles per second. The West component is -120 miles per second + (-40 miles per second), which is -160 miles per second.

Finally, we use these North and West components to find the resultant speed and direction of the airplane. The resultant speed is the magnitude of the resultant velocity, which is the square root of the sum of the squares of the North and West components. In this case, the resultant speed is √(0^2 + (-160)^2) = √25600 = 160 miles per second. The direction of the plane can be found using the tangent function: θ = arctan(W/N) = arctan(-160/0) = 90° south of west.