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?

Answer 1

Answer: 2.35 m/s

Step-by-step 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
`(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 * 3\\\Rightarrow L=6\pi\ m`

Tangential velocity is given by

`\Rightarrow v_t=(L)/(t)\\\\\Rightarrow v_t=(6\pi)/(8)\\\\\Rightarrow v_t=2.35\ m/s`

Thus, the tangential velocity is 2.35 m/s