You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighs 1515 lb and was traveling eastward. Car B weighs 1125 lb and was traveling westward at 45.0 mph. The cars locked bumpers and slid eastward with their wheels locked for 22.5 ft before stopping. You have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750. How fast (in miles per hour) was car A traveling just before the collision? (This problem uses English units because they would be used in a U.S. legal proceeding.)

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  1. east is positive
    1515 E -1125(45) = 2640 V

    F = 2640*.75 = -1980 pounds
    -1980 pounds = m a
    but m = 2640/g where g = 32.2 ft/s^2
    a = -(1980/2640)g = -.75 g = -24.15 ft/s^2
    = dv/dt
    0 = V-24.15 t so V =24.15 t
    22.5 = V t -12.07 t^2
    22.5 = 24.15 t^2 - 12.07 t^2 = 12.07 t^2
    t = 1.37 seconds
    V = 24.15 * 1.37 seconds = 33.1 ft/s
    convert that to mph
    33.1 ft/s = 22.6 mph
    now back to momentum
    1515 E -1125(45) = 2640 V
    1515 E = 50625+59664
    E = 72.8 mph

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