Question

You walk 49 m East, then 19 m North. What is the magnitude of your resultant vector?

Answer 1

The magnitude of the resultant vector after walking 49 m East and 19 m North is approximately 52.57 meters, calculated using the Pythagorean theorem.

Step-by-step explanation:

To find the magnitude of your resultant vector after walking 49 m East and then 19 m North, we will use the Pythagorean theorem as these two walks form the two perpendicular sides of a right-angled triangle. The resultant vector, often called the displacement vector, is the hypotenuse of this triangle. To calculate it:

• First, square both the eastward and northward displacements (49^2 and 19^2).
• Next, add these squared values.
• Finally, take the square root of this sum to get the magnitude of the resultant vector.

Calculating this gives us a magnitude of √(49^2 + 19^2) = √(2401 + 361) = √2762 ≈ 52.57 m. So, the magnitude of the displacement is approximately 52.57 meters.