A 26.2-kg dog is running northward at 3.02 m/s, while a 5.30-kg cat is running eastward at 2.74 m/s. Their 65.1-kg owner has the same momentum as the two pets taken together. Find the direction and magnitude of the owner's velocity.

Angle with the + x axis is θ = 79.599degree

Then the velocity of owner = 1.235m/s

Explanation:

Given that the mass of dog is m1 = 26.2 kg

velocity of dog is u1 = 3.02 m/s (north)

mass of cat is m2 = 5.3 kg

velocity is u2 = 2.74 m/s (east)

Mass of owner is M = 65.1 kg

Consider the east direction along + x axis andnorth along + y

momentum of dog is Py = m1 x u1

= 79.124 kg. m/s (j)

momentum of cat is Px = m2 x u2

= 14.522 kg. m/s (i)

Then the net magnitude of momentum is P = (Px2 + Py2) 1/2

= 80.445

Angle with the + x axis is θ = tan-1 (Py / Px) = 79.599 degree

Then the velocity of owner is v = P / M = 1.235 m/s