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Question: A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park...

A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometer per hour) is

A

0, 1

B

π+42,0\frac{\pi + 4}{2},0

C

21.4,π+4221.4,\frac{\pi + 4}{2}

D

0,21.40,21.4

Answer

0,21.40,21.4

Explanation

Solution

Net displacement of the cyclist = zero

Since the initial positions coincides with the final position.

Average speed of the cyclist

=Totaldistan⁡cetravelledTotaltimetaken=OP+PQ+QO10kmmin⁡−1=1+π2×1+110kmmin⁡−1=π+420kmmin⁡−1=π+420×60kmh−1=21.4kmh−1= \frac{Totaldis\tan cetravelled}{Totaltimetaken} = \frac{OP + PQ + QO}{10}km\min^{- 1} = \frac{1 + \frac{\pi}{2} \times 1 + 1}{10}km\min^{- 1}{} = \frac{\pi + 4}{20}km\min^{- 1} = \frac{\pi + 4}{20} \times 60kmh^{- 1} = 21.4kmh^{- 1}