Question

If a bus drives 3 km east, 5 km at 45° ne, 4 km at 20° nw, then 2 km south, what is the bus's resultant displacement?

Answer 1

Given : a bus drives 3 km east, 5 km at 45° ne, 4 km at 20° nw, then 2 km south,

To Find : bus's resultant displacement

Solution:

3 km east,  

EAST = 3 km

5 km at 45° ne  ( north East)

East = 5Cos45°  = 5/√2  km  = 3.54 km

North = 5Sin45°  = 5/√2  km =  3.54 km

4 km at 20° nw ( north West )

West = 4Cos20°  = 3.76 km  =  -  3.76 km EAST

North = 4Sin20°  = 1.37  km

2 km south,  = - 2 km North

NORTH = 3.54  +  1.37 - 3   = 2.91 km

EAST = 3 + 3.54 - 3.76  =  2.78 km

resultant displacement = √(2.91)² + (2.78)²  =  4.02 km

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