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30 August, 18:32

1000 Kg car approaches an intersection traveling north at 20 m/s. A 1150 Kg car approaches the same intersection traveling east at 33 m/s. The two cars collide at the intersection and lock together. Ignoring any external forces that act on the cars during the collision, what is the velocity of the cars immediately after the collision

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  1. 30 August, 20:12
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    We shall represent direction of east by unit vector i and direction of north by vector j

    momentum of 1000 kg car = mv j

    = 1000 x 20 j

    20000 j

    momentum of 1150 kg car = mvi

    = 1150 x 33 i

    = 37950 i

    Total momentum

    = 37950 i + 20000 j

    Let their common velocity be v after collision

    momentum after collision

    = (1000 + 1150) v

    = 2150v

    applying conservation of momentum law

    2150 v = 37950 i + 20000 j

    v = 17.65 i + 9.30 j

    magnitude of velocity

    = √ (17.65² + 9.3²)

    = 19.95 m / s

    direction θ with east

    tanθ = 9.3 / 17.65

    θ = 28 degree north of east.
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