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16 September, 15:47

A driver is traveling at 55 mi/h on a wet road. An object is spotted on the road 450 ft ahead and the driver is able to come to a stop just before hitting the object. Assuming standard perception/reaction time, determine the grade of the road.

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  1. 16 September, 16:42
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    G = + / - 0.0583 = + / - 5.83 %

    Explanation:

    Given:

    - Speed of the vehicle V = 55 mi/h

    - The spotting distance D = 450 ft

    - Assume standard perception/reaction time t = 2.5 s

    Find:

    Determine the grade of the road. When driver stops just before hitting the object.

    Solution:

    Step 1:

    Determine the distance d traveled for the perception reaction time t:

    d = V*t

    d = 55*1.467*2.5 = 201.7125 ft

    Step 2:

    The remaining distance left is the practical stopping distance SD:

    SD = D - d

    SD = 450 - 201.7125

    SD = 248.2875 ft

    Step 3:

    Calculate the grade G using practical stopping distance SD formula:

    SD = V^2 / [ 30 (a/g + / -G) ]

    (a/g + / -G) = V^2 / 30*SD

    G = + / - (V^2 / 30*SD - a/g)

    Where, a = 11.2 ft/s^2 and g = 32.2 ft/s^2 and V = 55 mph

    Plug in the values:

    G = + / - (55^2 / 30*248.2875 - 11.2/32.2)

    G = + / - 0.0583 = + / - 5.83 %
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