Question

On an open ground, a biker follows a track that turns to his left by an angle of 60° after every 600 m. Starting from a given turn, specify the displacement of the biker at the third and sixth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

Answer 1

The path followed by the biker will be a closed hexagonal path. Suppose the motorist starts his journey from the point O.

i. He takes the third at the point C.

= 1200 m

= 1.2 km 

∴ Total path length \(|\vec{OA}| + |\vec{AB}| + |\vec{BC}|\)

= 600 + 600 + 600 

= 1800 m 

= 1.8 km

The ratio of the magnitude of displacement to the total path-length = 1.2/1.8 = 2/3 = 0.67

ii. The motorist will take the sixth turn at O. 

Displacement is zero. 

path-length is = 3600 m or 3.6 km. 

Ration of magnitude of displacement and path-length is zero.