5 m/s east and 2.5 m/s North. What is resultant velocity?

To find the resultant velocity when two velocity vectors are given at right angles to each other, you can use the Pythagorean theorem. In this case, the velocities are 5 m/s east and 2.5 m/s north.

The magnitude of the resultant velocity \( v_r \) is calculated as:

\[
v_r = \sqrt{(5^2) + (2.5^2)} = \sqrt{25 + 6.25} = \sqrt{31.25} \approx 5.59 \, \text{m/s}
\]

Now, the direction \( \theta \) of the resultant velocity relative to the east direction can be found using:

\[
\theta = \tan^{-1} \left( \frac{2.5}{5} \right) = \tan^{-1} (0.5) \approx 26.57^\circ
\]

So, the resultant velocity is approximately 5.59 m/s at an angle of 26.57° north of east.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the angle between two vectors?
2. Can the resultant velocity be negative in any case?
3. What is the difference between speed and velocity?
4. How does the Pythagorean theorem apply to vector addition?
5. How would the result change if the vectors were not at right angles?

**Tip**: Always break velocity components into perpendicular directions to simplify calculations when vectors are involved.

Learn how to calculate the resultant velocity when given two perpendicular velocity vectors, 5 m/s east and 2.5 m/s north. This problem involves vector addition using the Pythagorean theorem and trigonometry to find both magnitude and direction. Suitable for students in Grades 9-12.

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