Question

A cyclist starts from the center O of a circular park of radius I km, reaches the edge P of the park, then cycles along the circumference and returns to the center along Q0 as shown in figure. If the round trip takes 10 minutes, then the average speed of cyclist is?

Figure and option here​

Answer 1

Answer:

option (2)

Step-by-step explanation:

average speed = total distance ÷ total time

Vav= (πr/2+2)km/10 mins

=π+4/20 km/min

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Answer 2

$\huge{ \boxed{ \mathtt{ \purple{Solution}}}}$

${\boxed{\mathtt{\purple{Given}}}}$

Total time taken in trip = 10 min

Total distance = QO + OP + PQ

Length of radius ( OP and QO) = 1 km each

_________________________

$\boxed{formula \: = \: \frac{total \: distance}{total \: time} }$

As we know that circumference of a circle is 2πr .

And there are 4 quarter in a circle of circumference of each quarter will be equal to :-

Circumference of quarter circle( PQ) = 2πr/4

$\implies \: \frac{2.\pi.r}{4}$

$\implies \: \frac{2.\pi.1}{4}$

$\implies \: \frac{\pi}{2}$

Total distance = 1 + 1 + π/4

Total distance = 2 + π/4

Total time = 10 minutes

$\implies \: Speed \: = \frac{ \frac{\pi}{2} + 2}{10}$

$\implies \: \frac{4 + \pi}{2} \times \frac{1}{10}$

$\boxed{ \red{Average\: Speed \: = \: \frac{4 + \pi}{20} \: km \: per \: min}}$