Question

A 19.3 kg dog is running northward at 2.98 m/s , while a 6.26 kg cat is running eastward at 3.64 m/s . Their 78.7 kg owner has the same momentum as the two pets taken together. You may want to review. Find the direction and magnitude of the owner's velocity.

Answer 1

Answer:

v = 0.78 m/sec at 21.61° towards the east of north

Explanation:

Given a 19.3 kg dog is running northward at 2.98 m/s , while a 6.26 kg cat is running eastward at 3.64 m/s and the mass of the owner is 78.7 kg.

Given m(dog) = 19.3 kg and m(cat) = 6.26 kg

v(dog) = $2.98\vec{j}$ m/sec

v(cat) =  $3.64\vec{i}$ m/sec

Given the $\vec{P}(owner)=\vec{P}(dog)+\vec{P}(cat)$

Let the velocity of the owner be $\vec{v}$

We know that $\vec{P}=m\vec{v}$

$m(owner)\times \vec{v}=m(dog)\times \vec{v(dog)}+m(cat)\times \vec{v(cat)}$

$78.7\times \vec{v}=19.3\times 2.98\vec{j}+6.26\times 3.64\vec{i}$

$\vec{v}=\frac{1}{78.7}(57.5\vec{j}+22.78\vec{i})$

$v=\sqrt{(\frac{57.5}{78.7})^2+(\frac{22.78}{78.7})^2  }$

v=0.78 m/sec

for direction

Tan(α)=$\frac{component of x}{component of y}$

where α is the angle toward east of north.

Tan(α)=$\frac{22.78}{57.5}$

α=21.61°