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8 February, 03:14

A car traveling north at 10.0 m/s crashes into a car traveling east at 15 m/s at an unexpectedly icy intersection. The cars lock together as they skid on the ice. The two cars have the same mass. What is their combined speed after the collision?

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  1. 8 February, 07:00
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    The first thing you should know is the conservation of the linear momentum

    Pi = Pf

    We have then that before the shock:

    Pi = mvi1 + mvi2 = m (10.0) j + m (15.0) i

    We have after the shock:

    Pf = 2mvf = 2mv (sinx) j + 2mv (cosx) i

    Matching both expressions:

    m (10.0) j + m (15.0) i = 2mv (sinx) j + 2mv (cosx) i

    Rewriting

    (10.0) j + (15.0) i = 2v (sinx) j + 2v (cosx) i

    We have 2 equations (components j and i) and two unknowns (angle x and v)

    2v (senx) = 10.0

    2v (cosx) = 15.0

    Resolving:

    tanx = (10.0 / 15.0)

    x = atan (10.0 / 15.0) = 33.69 degrees

    Clearing v

    2v (senx) = 10.0

    v = (10.0 / 2) * (1 / sen (33.69)) = 9.01 m / s

    answer

    their combined speed after the collision is 9.01 m / s in the direction 33.69 degrees
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