Question

A dog is sniffing around for a bone. He walks 3.6 m east and 6.0 m north. What are the magnitude and direction of the dog from his original position?

Answer 1

Vectorial form:

3.6 m east => 3i

6.0 north => 6 j

Final position = 3.6i + 6j

Magnitude = √[ (3.6)^2 + 6^2] = √[12.96 + 36] = √48.96 = 7.0 m

Direction => arc tan (6/3.6) = arc tan (1.67) = 59.0 °

Answer: the dog is at 7.0 m, 59.0° to the north of the east from the starting point.