Two cars approach each other from 500 m apart, each at 20 m/s. A bird flies between them at 30 m/s. Whenever it reaches a car it rests there for 1 s before starting towards the other car. Count only completed inter-car flights. How many complete flights does it make before the cars meet?
Physics · Kinematics part-3 Relative motion · Relative motion in one dimension
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Question

Two cars approach each other from 500 m apart, each at 20 m/s. A bird flies between them at 30 m/s. Whenever it reaches a car it rests there for 1 s before starting towards the other car. Count only completed inter-car flights. How many complete flights does it make before the cars meet?

Physics · Kinematics part-3 Relative motion · Relative motion in one dimension

G1 Physics · Accepted Answer

Cars meet after 500/(20+20)=12.5 s. First bird flight takes 500/(30+20)=10 s. Separation is then 100 m. During the 1 s rest it becomes 60 m. Second flight takes 60/50=1.2 s, reaching t=12.2 s. Only 0.3 s remains before the cars meet, so the next 1 s rest cannot finish. Hence the bird completes exactly 2 flights.