A dog is running in a circle around a tree, trying to catch a rabbit. The dog’s owner notices the dog completes 4 laps around the tree

Question

A dog is running in a circle around a tree, trying to catch a rabbit. The dog’s owner notices the
dog completes 4 laps around the tree in 32 seconds and the radius of the dog’s circular path is
3 meters. What is the tangential velocity of the dog?

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Xavia 3 years 2021-08-10T21:17:52+00:00 1 Answers 8 views 0

Answers ( )

  1. quangkhai
    0
    2021-08-10T21:19:27+00:00
    Reply

    Answer: 2.35 m/s

    Explanation:

    Given

    Dog completes 4 laps around the tree in  32 seconds

    Radius of the circular path is 3 m

    Time period for single lap is  \frac{32}{4}=8\ s

    Length of the track is equivalent to the perimeter of the path

    \Rightarrow L=2\pi r\\\Rightarrow L=2\pi \times 3\\\Rightarrow L=6\pi\ m

    Tangential velocity is given by

    \Rightarrow v_t=\dfrac{L}{t}\\\\\Rightarrow v_t=\dfrac{6\pi}{8}\\\\\Rightarrow v_t=2.35\ m/s

    Thus, the tangential velocity is 2.35 m/s

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