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three dogs sitting at the vertices of an equilateral triangle. The length of each side of the triangle equals to s meters. A person gives the command "Start!" and each dog starts to run with constant speed v meters per second. At each moment, each dog is running towards the dog just right to him (in counter-clockwise direction). Therefore, their trajectories are forming some spirals that converging to one point as illustrated below. How long does it takes dogs to meet each other after the command "Start!"?

three dogs sitting at the vertices of an equilateral triangle. The length of each side of the triangle equals to s meters. A person gives the command "Start!" and each dog starts to run with constant speed vmeters per second. At each moment, each dog is running towards the dog just right to him (in counter-clockwise direction). Therefore, their trajectories are forming some spirals that converging to one point as illustrated below.
How long does it takes dogs to meet each other after the command "Start!"?

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Grade:12

3 Answers

Tushar
16 Points
7 years ago
In a above question let us assume on sog at rest now component of first dog along o ther dog(assumed to be at rest ) so
Tushar
16 Points
7 years ago
Speed is vcos60 now we have distance =d and speed equal vcos60 so time is t=d/vcos60 that is 2d/v . Tell me if answer is wrong
Piyush Kumar Behera
417 Points
7 years ago
In this type of question you can just find the velocity at which the separation b/w them is reduced,that is the net contribution of of all the velocities along the line joining both the dogs.so the answer will come as 2d/v

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