To find the resultant of two vectors, one pointing **50 units west** and the other **50 units south**, we can treat them as perpendicular vectors and use the **Pythagorean theorem**. The two vectors form a right triangle, with the resultant vector being the hypotenuse.

### Step-by-step process:

1. The magnitudes of both vectors are 50 units.
2. Since they are perpendicular, we can calculate the magnitude of the resultant vector using:
   \[
   R = \sqrt{50^2 + 50^2}
   \]
   \[
   R = \sqrt{2500 + 2500} = \sqrt{5000} \approx 70.71 \, \text{units}
   \]

3. Now, we need to find the direction of the resultant. The direction can be given by the angle \( \theta \) with respect to either the west or south direction. Using the tangent function:
   \[
   \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{50}{50} = 1
   \]
   \[
   \theta = \tan^{-1}(1) = 45^\circ
   \]
   
Thus, the resultant vector has a magnitude of **70.71 units** and a direction of **45° south of west** (or **45° west of south**).

### Result:
- **Magnitude:** 70.71 units
- **Direction:** 45° south of west

Would you like more details or have any questions?

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Here are 5 related questions for further exploration:

1. How do you find the resultant of two vectors if they are not perpendicular?
2. What happens if the magnitudes of the vectors are different?
3. How do you add vectors graphically using the head-to-tail method?
4. Can you explain the role of trigonometry in finding vector resultants?
5. How would you find the resultant of vectors in three dimensions?

**Tip:** The magnitude of a resultant vector from perpendicular components can always be found using the Pythagorean theorem.

Learn how to calculate the resultant of two perpendicular vectors, 50 units west and 50 units south, using the Pythagorean theorem and trigonometry. The magnitude is 70.71 units, and the direction is 45° south of west. Suitable for Grades 9-11.

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