How to Calculate the Magnitude of Resultant Velocity for a Kayaker

What are the velocities and angles of the kayaker's paddling?

The kayaker paddles at 4.0 m/s in a direction 30° south of west and then at 3.7 m/s in a direction 20° west of south.

Calculating the Magnitude of Resultant Velocity

When a kayaker paddles at different velocities and angles, we can calculate the magnitude of the kayaker's resultant velocity by using vector addition. Let's break down the velocities into their horizontal and vertical components to find the resultant velocity.

Understanding Vector Addition for Kayaker's Resultant Velocity

When the kayaker paddles at 4.0 m/s in a direction 30° south of west, the velocity can be broken down into an x-component of -3.46 m/s and a y-component of -2 m/s. Similarly, when the kayaker paddles at 3.7 m/s in a direction 20° west of south, the velocity can be broken down into an x-component of -3.54 m/s and a y-component of -1.28 m/s.

By adding the x-components and y-components separately, we can determine the resultant velocity in the x and y directions. The x-component of the resultant velocity would be -3.46 m/s - 3.54 m/s = -7.00 m/s, while the y-component would be -2 m/s - 1.28 m/s = -3.28 m/s.

Finally, using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity: √((-7.00 m/s)² + (-3.28 m/s)²) ≈ 7.7 m/s. Therefore, the magnitude of the kayaker's resultant velocity is approximately 7.7 m/s.