Question

A 26.2-kg dog is running northward at 3.21 m/s, while a 5.30-kg cat is running eastward at 2.64 m/s. Their 67.2-kg owner has the same momentum as the two pets taken together. Find the direction and magnitude of the owner's velocity.

Answer 1

Answer:

v=1.26 m/s

Θ=81°NE

Explanation:

Linear momentum is the product of the mass and velocity of an object.

$p=mv$

Dog's momentum can be hold using its mass and velocity:

m=26.2kg

v=3.21 m/s

$P_{dog} =26.2*3.21=84.102$ (kg⋅m/s)

same thing with the cat

m=5.30kg

v=2.64m/s

$P_{cat} = 5.30*2.64=13.992$ (kg⋅m/s)

owner's momentum

p =13.992 m/s i + 84.102 m/s j  

divide by mass to get velocity:  

v = 0.20m/s i + 1.25 m/s j  

mag v = √(0.20² + 1.25²) m/s = 1.26 m/s  

Θ = arctan(1.25/0.2) = 81º north of east