Resultant Velocity: A Combination of Forces

What is the resultant velocity of an airplane heading north at 100 m/s with a crosswind blowing at 30 m/s from east to west?

Calculate the resultant velocity of the airplane.

Resultant Velocity Calculation:

To determine the resultant velocity of the airplane, we need to consider the velocities as vectors and combine them.

When an airplane is moving in one direction while facing a crosswind from another direction, the resultant velocity is the combination of both velocities. In this case, the airplane is heading north at 100 m/s and there is a crosswind blowing from east to west at 30 m/s.

To calculate the resultant velocity, we need to break down the velocities into their horizontal and vertical components. The northward velocity of 100 m/s does not have a horizontal component, while the crosswind of 30 m/s has a horizontal component of 30 m/s and no vertical component.

Using vector addition, we can add the horizontal components of both velocities to get the horizontal component of the resultant velocity. This can be done by using the Pythagorean theorem and trigonometric functions to find the magnitude and direction of the resultant velocity:

Magnitude: √(100^2 + 30^2) ≈ 104.40 m/s

Direction: arctan(30/100) ≈ 6.34 degrees north of due west

Therefore, the resultant velocity of the airplane is approximately 104.40 m/s with a direction of about 6.34 degrees north of due west.