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5 August, 18:43

You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighs 1515 1515 lb and was traveling eastward. Car B weighs 1125 1125 lb and was traveling westward at 44.0 44.0 mph. The cars locked bumpers and slid eastward with their wheels locked for 20.5 20.5 ft before stopping. You have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750 0.750. How fast (in miles per hour) was car A traveling just before the collision

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Answers (2)
  1. 5 August, 19:27
    0
    72.8mph

    Explanation:

    east is positive

    1515 E - 1125 (45) = 2640 V

    F = 2640*.75 = - 1980 pounds

    so

    -1980 pounds = m a

    but m = 2640/g where g = 32.2 ft/s^2

    so

    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

    so

    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
  2. 5 August, 19:56
    0
    Speed = 72.76mph

    Explanation:

    east direction signifies +

    Therefore,

    1515E - 1125 (45) = - 2640

    F = - 2640*0.75 = - 1980lbs

    so,

    -1980lbs = Ma

    but m = 2640*g where g = 32.2 ft/s²

    so,

    a = - (1980/2640g) = - 0.75*g = - 24.15ft/s² = dv/dt

    0 = V-24.15t

    V = 24.15t

    22.5 = Vt - 12.07t²

    22.5 = 24.15t² - 12.07t² = 12.07t²

    t = 1.37 seconds

    Therefore,

    V = 24.15 * 1.37 seconds = 33.1 ft/s

    converting to mph gives

    33.1 ft/s = 22.6 mph

    now back to momentum

    1515 E - 1125 (45) = 2640 V

    1515 E = 50625+59664

    Speed = 72.76 mph
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