Question

an airplane heads northwest at an airspeed of 500 km/hr, but there is a wind blowing from the west at 50 km/hr. what is the i component of the resulting vector (in km/hr) you get from adding the vectors of the heading of the plane and the wind? round your answer to one decimal place. do not write km/hr.

Answer 1

the i-component of the resulting vector is approximately 353.6 km/hr.

Step-by-step explanation:

Given:

Airplane's airspeed: 500 km/hr (heading northwest)

Wind speed: 50 km/hr (blowing from the west)

To find the i-component of the resulting vector, we can break down the vectors into their horizontal and vertical components.

The airplane's airspeed can be broken down into its horizontal (i) and vertical (j) components as follows:

Airplane's airspeed (horizontal component) = Airspeed * cos(angle)

Since the airplane is heading northwest, the angle between the airspeed vector and the positive x-axis is 45 degrees.

Airspeed (horizontal component) = 500 km/hr * cos(45°)

The wind speed is already a horizontal vector blowing from the west, so its i-component is simply -50 km/hr.

To find the resulting i-component, we add the horizontal components of the airspeed and the wind:

Resulting i-component = Airspeed (horizontal component) + Wind speed (i-component)

Resulting i-component = 500 km/hr * cos(45°) + (-50 km/hr)

Calculating this expression gives us the i-component of the resulting vector. Rounding the answer to one decimal place, we have:

Resulting i-component ≈ 353.6 km/hr