Question

Two bicyclists begin to travel clockwise on a circular path of diameter ?=110.00 mD=110.00 m with the constant speeds ?A=10.00 m/svA=10.00 m/s and ?B=8.00 m/s,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 ?P=15.00 m/s.vP=15.00 m/s. Upon reaching cyclist A, the pigeon instantly flies back towards cyclist B at the same speed until it reaches the location of cyclist B at that time. The pigeon then flies back again to cyclist A, and so on until the two bicyclists meet.

What is the total distance traveled by the pigeon?

Answer 1

diameter = 110 m

circumference = d = * 110 = 345.57 m

so,

arc distance between cyclists = C / 2 = 172.78 m

Let cyclists B travels distance 'd' before meeting up with cyclist A

so,

time taken by A = ( d + 172.78) / 10

time taken by B = d / 8

as time taken must be same, so

( d + 172.78) / 10 = d / 8

d + 172.78 = 1.25d

172.78 = 0.25d

so,

d = 691.12 m

so,

time taken, t = 691.12 / 8 = 86.39 seconds

Therefore,

distance traveled by pigeon

d = v_p * t

d = 15 * 86.39

d = 1295.85 m