Question

a man lost in a maze makes three consecutive displacements so that at the end of the walk he is right back wherehe started. the first displacement is 8.00 m westward, and the second is 13.0 m northward. find the magnitude and direction of the third displacement.

Answer 1

To find the magnitude and direction of the third displacement, we can use vector addition. The first displacement is 8.00 m westward and the second is 13.0 m northward. The magnitude of the third displacement is 5.00 m and it is in the opposite direction of the displacement vectors A and B.

Step-by-step explanation:

To find the magnitude and direction of the third displacement, we can use vector addition. The first displacement is 8.00 m westward and the second is 13.0 m northward. We can represent these displacements as vectors A and B.

Vector A = -8.00 m (westward)
Vector B = 13.0 m (northward)

To find the third displacement, we need to find the vector that will bring us back to the starting point, which means the total vector sum should be equal to zero.

So, we have A + B + C = 0

Plugging in the values of A and B, we get:
-8.00 m + 13.0 m + C = 0
5.00 m + C = 0
C = -5.00 m

The magnitude of the third displacement is 5.00 m and it is in the opposite direction of the displacement vectors A and B.