Two bicyclists begin to travel clockwise on a circular path of diameter D = 150.

Question

Two bicyclists begin to travel clockwise on a circular path of diameter D = 150.00 m with the constant speeds vA = 11.00 m/s and vB = 8.00 m/s, respectively, from two points diametrically opposed. A pigeon released from the starting point of cyclist B flies directly toward cyclist A at a constant speed vP = 16.50 m/s. Upon reaching him, the pigeon returns instantly towards cyclist B flying with the same speed until it reaches his location at that time, and then it turns again towards cyclist A, and so on until the two bicyclists meet. What is the total distance travelled by the pigeon?

Explanation / Answer

given velocity of A= Va=11.0 m/s

and that of Vb=8.0 m/s

also diameter of circle=150.0 m

so radius= 75.0 m

so circumference of circle= C=2*p*75=471.238 mlet

therefore C/2=235.62 m

so cyclist B travel d distansce before meeting cyclist A

so distance travelled by cyclist A=d+235.63

as time taken by both is same so by equating boths time we get

time taken by A=(d+235.62)/11

time taken by B=d/8

so (d+235.62)/11=d/8

(d/11)+(235.62/11)=d/8

solving we get d=628.32 m

and time taken by them= 628.32/8=78.54 sec

the pigeon will also take same time

and given velocity of pigeon Vp= 16.5 m/s

so distance travelled by pigeon= 16.5*78.54=1295.91 m

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