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13 April, 01:48

The stoplight had just changed and a 1800 kg Cadillac had entered the intersection, heading north at 4.0 m/s, when it was struck by a 1200 kg eastbound Volkswagen. The cars stuck together and slid to a halt, leaving skid marks angled 35∘ north of east. How fast was the Volkswagen going just before the impact?

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  1. 13 April, 02:10
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    Answer: 8.6 m/s

    Explanation:

    Assuming no external forces present during the collision, total momentum must be conserved.

    As momentum is a vector, if we decompose it in two perpendicular components (one N-S and the other W-E), total momentum must be conserved for both directions.

    Prior to collision, the only component in the eastbound direction was due to the Volkswagen:

    px = mvolk. Vvolk = 1,200 kg. Vvolk

    After the collision, we have a component along this axis, which is the projection of the momentum vector due to both cars stuck together, 35º north of the east:

    pxf = (mvolk + mcad). vf. cos 35º (1)

    With this same reasoning, we can write the following equation for the momentum on the N-S axis:

    py1 = 1,800 kg. 4.0 m/s = (1,800 + 1,200) kg. Vf. sin 35º (2)

    Dividing both sides in (2) and (1), we get:

    1,800. 4.0 / 1,200. Vvolk = tg 35º

    Solving for Vvolk:

    Vvolk = 7,200 / 1,200. tg 35º = 8.6 m/s
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