Question

A 30.0 kg dog is running northward at 2.14 m/s, while a 4.86 kg cat is running eastward at 2.97 m/s. Their 75.2 kg owner has the same momentum as the two pets taken together.

Part A) Find the direction of the owner's velocity (in degrees north of east).

Part B) Find the magnitude of the owner's velocity (in m/s).

Answer 1

mass of dog m = 30 kg

Velocity of the dog v = 2.14 j

Mass of cat M = 4.86 kg

Velocity of the cat V = 2.97 i

Where i , j are the unit vectors along east and north directions respectively.

Mass of owner M ' = 75.2 kg

Momentum of the owner P = mv + MV

= 30(2.14 j ) + 4.86 ( 2.97 i )

= 64.2 j + 14.4342 i

Velocity of the owner V ' = P / M '

= ( 64.2 j + 14.4342 i) / 75.2

= 0.191944 i + 0.8537 j

Let V ' makes an angle with east then tan = 0.8537 / 0.191944

= 4.44

= 77.32 ^o

(b). Magnitude of the owner velocity = [0.8537 ² + 0.191944 ² ]

= 0.875 m/s