Question

a kayaker paddles at 4.0 m/s in a direction 30° south of west. he then turns and paddles at 3.7 m/s in a direction 20° west of south. What is the magnitude of the kayaker’s resultant velocity? Round your answer to the nearest tenth.

Answer 1

To find the magnitude of the kayaker's resultant velocity, we can use vector addition. We can break down each velocity vector into its horizontal and vertical components.

Step-by-step explanation:

To find the magnitude of the kayaker's resultant velocity, we can use vector addition. We can break down each velocity vector into its horizontal and vertical components.

The kayaker's first velocity vector is 4.0 m/s at 30° south of west. This can be split into a horizontal component of 4.0 * cos(30°) and a vertical component of 4.0 * sin(30°).

The kayaker's second velocity vector is 3.7 m/s at 20° west of south. This can be split into a horizontal component of 3.7 * sin(20°) and a vertical component of 3.7 * cos(20°).

To find the resultant velocity, we add the horizontal components and the vertical components separately, then use the Pythagorean theorem to find the magnitude.

Answer 2

The magnitude of the kayaker's resultant velocity is approximately 7.7 m/s.

Step-by-step explanation:

To find the magnitude of the kayaker's resultant velocity, we can break down the velocities into their x and y components. The first velocity of 4.0 m/s at a direction 30° south of west can be broken down into an x-component of -3.46 m/s and a y-component of -2 m/s. The second velocity of 3.7 m/s at a direction 20° west of south 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 find 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. The y-component of the resultant velocity would be -2 m/s - 1.28 m/s = -3.28 m/s.

Finally, we can find the magnitude of the resultant velocity using the Pythagorean theorem: √((-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.