A 26-kg dog is running northward at 2.7 m/’s, while a 5.3 kg cat is running eastward at 3.0 m/s.

Question

A 26-kg dog is running northward at 2.7 m/’s, while a 5.3 kg

cat is running eastward at 3.0 m/s.

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Jezebel 2 months 2021-07-31T20:21:13+00:00 1 Answers 6 views 0

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    2021-07-31T20:22:31+00:00

    Answer:

    Question

    A. Find the total momentum of the system

    B. Find the magnitude of the total momentum

    Explanation:

    Momentum can be defined as the product of mass and velocity, it is a vector quantity.

    Momentum = mass × velocity

    P = mv

    So, since it is a vector quantity we must take note of its direction

    Given that,

    1. 26-kg dog is running northward at 2.7 m/’s

    Md = 26kg

    Vy = 2.7m/s •j

    Then, it is moving in the positive y direction

    Then, it is momentum is

    Py = Md•Vy

    Py = 26 × 2.7 •j

    Py = 70.2 kgm/s •j

    2. A 5.3 kg cat is running eastward at 3.0 m/s.

    The cat is running towards the east, then it is moving in the positive x direction

    Vx = 3 •i m/s

    Mc = 5.3kg

    Px = Mc•Vx

    Px = 5.3 × 3 •i

    Px = 15.9 •i kgm/s

    Then,

    Total momentum is equal to

    P = Px + Py

    P = 15.9 •i + 70.2 •j kgm/s

    B. Magnitude of the total momentum

    Magnitude of a vector quantity

    x = a•i + b•j is generally given as

    X = √(a²+b²)

    Direction <X = arctan(b/a)

    Therefore,

    |P| = √(15.9²+70.2²)

    |P| = 71.98 kgm/s

    Direction

    <P = arctan(Py/Px) =arctan(70.2/15.9)

    <P = 77.24°

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