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15 June, 10:28

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.

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  1. 15 June, 11:12
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    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
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