Question

A 27.4 kg dog is running northward at 2.19 m/s , while a 7.19 kg cat is running eastward at 2.78 m/s . Their 75.7 kg owner has the same momentum as the two pets taken together. Find the direction and magnitude of the owner's velocity.

Answer 1

`\| \vec v\| = 0.836\,(m)/(s)`,
`\alpha = 71.577^(\textdegree)` (Northeast)

Step-by-step explanation:

Let consider that owner has the resultant direction of the momentums from the dog and the cat. First, the momentum of the owner is:

`\|\vec p \| = \sqrt{\left[(27.4\,kg)\cdot \left(2.19\,(m)/(s) \right)\right]^(2)+\left[(7.19\,kg)\cdot \left(2.78\,(m)/(s) \right)\right]^(2)}`

`\|\vec p \| = 63.248\,kg\cdot (m)/(s)`

The speed of the owner is:

`\|\vec v \| = (63.248\,kg\cdot (m)/(s))/(75.7\,kg)`

`\| \vec v\| = 0.836\,(m)/(s)`

Lastly, the direction of the owner is:

`\alpha = \tan^(-1)\left[((27.4\,kg)\cdot \left(2.19\,(m)/(s) \right))/((7.19\,kg)\cdot \left(2.78\,(m)/(s) \right)) \right]`

`\alpha = 71.577^(\textdegree)` (Northeast)