A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which…
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point?
An angle less than 45° South of East
An angle less than 45° North of East
An angle more than 45° South of East
An angle more than 45° North of East
Solution
Net North displacement = 12 - 6 = 6 km; net East displacement = 8 km. The final point is North-East of the start, with the East component (8) greater than the North component (6). Since the angle opposite the larger side is greater, the angle from the East axis is less than 45°. Hence she is at an angle less than 45° North of East.