A bicyclist travels $4.5\text{ km}$ west, then travels $6.7\text{ km}$ at an angle $27.0^\circ$ South of West. What is the magnitude of the bicyclist's total displacement?

10.88 km

Explanation:

We shall represent displacement in terms of i , j  unit vectors in the direction of east and north .

4.5 km due west

D₁ = - 4.5 i

6.7 km at an angle of 27° south of west

D₂ = - 6.7 cos27 i - 6.7 sin27j

= - 6.7 x .89 i - 6.7 x .45 j

= - 5.96i - 3 j

Total displacement

= D₁ + D₂

=  - 4.5 i - 5.96i - 3 j

= -10.46 i - 3j

Magnitude = √ ( 10.46² + 3²)

= √ ( 109.41 + 9)

= √ 118.41

= 10.88 km .

0.11 m/s and 0.28 m/s should be correct