How to Calculate the Magnitude and Direction of Resultant Velocity for a Kayaker

What is the magnitude of the kayaker’s resultant velocity? Round your answer to the nearest tenth.

___m/s

What is the direction of the kayaker’s resultant velocity?

___ ° south of west

Final answer:

The magnitude of the resultant velocity is determined by converting the velocities to their component parts and adding them up. The magnitude is the square root of the sum of the squares of the resultant components. The direction of the velocity can be calculated by finding the inverse tangent of the ratio of the southward component to westward component of the resultant velocity.

Explanation:

To find the magnitude and direction of resultant velocity, we must first convert each velocity to its components i.e. westward and southward. Let's denote westwards as negative and southwards as positive.

Firstly, for a velocity of 4 m/s 30° south of west. The westward component is -4 cos 30° and the southward component is 4 sin 30°.

Secondly, for a velocity of 3.7 m/s 20° west of south. The westward component is -3.7 sin 20° and the southward component is 3.7 cos 20°.

Adding up the components, we find the resultant westward component = (-4 cos 30°) + (-3.7 sin 20°) and resultant southward component = (4 sin 30°) + (3.7 cos 20°).

The magnitude of resultant velocity is the square root of sum of squares of these components, which you can calculate and round to nearest tenth. The direction of this velocity can be obtained by finding the inverse tangent of the ratio of the southward to the westward component in the resultant velocity.