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BigorU [14]
2 years ago
10

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 t

he same momentum as the two pets taken together. You may want to review. Find the direction and magnitude of the owner's velocity.
Physics
1 answer:
m_a_m_a [10]2 years ago
3 0

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°

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