Question

A robot starts from a certain point and moves east for a distance of 5.0 meters, then goes north for 3.0 meters, and then turns west for 2.0 meters. a. What are the x-y coordinates for the resultant vector? b. What is the magnitude of the resultant vector for the robot?

Answer 1

Explanation:

It is given that, a robot starts from a certain point and moves east for a distance of 5.0 meters, then goes north for 3.0 meters, and then turns west for 2.0 meters.

Let east is +x, west is -x north is +y.

When it moves east for a distance of 5.0 meters, it means (5,0)

When it goes north for 3.0 meters, and then turns west for 2.0 meters, it means (0,3) +(-2,0)

(a) x-y coordinates for the resultant vector is (3,3)

(b) The magnitude of the resultant vector for the robot is given by :

$R=\sqrt{3^2+3^2} \\\\R=4.24\ m$