Question

A driver travels 4.1 km west, 17.3 km north, and finally 1.2 km at an angle of 65.4 degree north of west. What is the driver’s displacement?

Answer 1

Answer:

Explanation:

We shall represent each displacement in vector form .

i will represent east , j will represent north .

D₁ = 4.1 west = - 4.1 i

D₂ = 17.3 north = 17.3 j

D₃ = - 1.2 cos65.4 i + 1.2 sin65.4 j

= - .5 i + 1.09 j

Total displacement

= D₁ + D₂ + D₃

=  - 4.1 i + 17.3 j - .5 i + 1.09 j

D = - 4.6 i + 18.39 j

magnitude of D

= √ ( 4.6² + 18.39² )

= √ (21.16 + 338.2 )

= √359.36

= 18.95 km .

Final displacement = 18.95 km .