Question

4) A 26.2-kg dog is running northward at 2.70 m/s, while a 5.30-kg cat is running eastward at 3.04 ms. Their 74.0-kg owner has the same momentum as the two pets taken together. Find the direction and magnitude of the owner’s velocity.

Answer 1

Linear momentum (p) :

p= m v

where:

m= mass

v=velocity

Cat's momentum:

Pcat = 5.30 x 3.04 = 16.112 kgm/s

Dog's momentum:

Pdog = 26.2kg x 2.70 m/s= 70.74 kg m/s

Owner's momentum:

Pcat + Pdog = 16.112 m/s j+ 70.74 m/s i

Divide by mass of the owner

v = ( 16.112 m/s j+ 70.74 m/s i ) / 74 kg

v owner = 0.21 m/s i + 0.955 m/s j

Use the components to find the velocity

V owner = √(0.21 m/s )^2 + (0.955 ^2 m/s)^2 )

V owner = 0.98 m/s

Arc tan = 0.955/0.21 = 77.1° North of east