Question

A person moves 30 m north, then 20 m towards east, and finally 30√2 m in the southwest direction. The displacement of the person from the origin will be:

(a) 40 m, southeast
(b) 40 m, southwest
(c) 20 m, southeast
(d) 20 m, southwest

Answer 1

To find the displacement of the person from the origin, we need to add the vectors representing each movement together. The displacement of the person from the origin will be -30√2 m in the x-direction and 0 m in the y-direction, representing a movement towards the southwest direction.

Step-by-step explanation:

To find the displacement of the person from the origin, we need to add the vectors representing each movement together. Let's break down each movement into its x and y components.

The person moves 30 m north, which has a y-component of 30 and an x-component of 0.

Then, the person moves 20 m towards the east, which has a y-component of 0 and an x-component of 20.

Finally, the person moves 30√2 m in the southwest direction, which has a y-component of -30 and an x-component of -30√2.

Now, we can add the x-components and the y-components separately to find the total displacement.

x-component: 0 + 20 + (-30√2) = -30√2

y-component: 30 + 0 + (-30) = 0

The displacement of the person from the origin will be -30√2 m in the x-direction and 0 m in the y-direction.

So, the displacement is -30√2 m, which represents a movement towards the southwest direction.