Question

A woman travels a distance of 1m towards north then 2m towards east and finally 3m towards south .Find total distance and displacement.

Answer 1

ANSWER:

• Total distance = 6 m

• Total displacement = 2√2 m

GIVEN:

• A woman travels a distance of 1 m towards north

• 2 m towards east

• 3 m towards south

TO FIND:

• Total distance

• Total displacement

EXPLANATION:

DISTANCE:

• Distance is the actual length or total length traversed by a body.

• It is a scalar as it has only magnitude but no specific direction.

Total distance travelled = 1 m + 2 m + 3 m = 6 m

DISPLACEMENT:

• Displacement is the shortest distance travelled by the body.

• It is a vector as it both only magnitude and specific direction.

Let ABCD be the path travelled by the woman

Displacement = AD

By using Pythagoras theorem

AD² = AF² + FD²

AF = BC = 2 m

FD + FC = CD = 3 m

FC = AB = 1 m

1 + FD = 3

FD = 2 m

Substitute FD = 2 m and AF = 2 m in AD² = AF² + FD²

AD² = 2² + 2²

AD² = 4 + 4

AD² = 8

AD = √8

AD = 2√2

Total Displacement travelled = 2√2 m

NOTE: REFER ATTACHMENT FOR DIAGRAM.