Two vehicles approach an intersection, a 2500kg pickup travels from E to W at 14.0m/s and a 1500kg car from S to N at 23.0m/s. Find P net of

Question

Two vehicles approach an intersection, a 2500kg pickup travels from E to W at 14.0m/s and a 1500kg car from S to N at 23.0m/s. Find P net of this system (direction and magnitude)

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Tryphena 3 years 2021-08-14T20:07:51+00:00 1 Answers 28 views 0

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  1. Helga
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    2021-08-14T20:09:37+00:00
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    Answer:

    The magnitude of the momentum is 49145.19 kg.m/s

    The direction of the two vehicles is 44.6° North West

    Explanation:

    Given;

    speed of first vehicle, v₁ = 14 m/s (East to west)

    mass of first vehicle, m₁ = 1500 kg

    speed of second vehicle, v₂ = 23 m/s (South to North)

    momentum of the first vehicle in x-direction (E to W is in negative x-direction)

    P_x = mv_x\\\\P_x = 2500kg(-14 \ m/s)\\\\P_x = -35000 \ kg.m/s

    momentum of the second vehicle in y-direction (S to N is in positive y-direction)

    P_y = m_2v_y\\\\P_y = 1500kg(23 \ m/s)\\\\P_y = 34500 \ kg.m/s

    Magnitude of the momentum of the system;

    P= \sqrt{P_x^2 + P_y^2} \\\\P = \sqrt{(-35000)^2+(34500)^2} \\\\P = 49145.19 \ kg.m/s

    Direction of the two vehicles;

    tan \ \theta = \frac{P_y}{|P_x|} \\\\tan \ \theta = \frac{34500}{35000} \\\\tan \ \theta = 0.9857\\\\\theta = tan^{-1} (0.9857)\\\\\theta = 44.6^0North West

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