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9 September, 15:00

Two forces with magnitudes of 100 and 50 pounds act on an object at angles of 50° and 160° respectively. Find the direction and magnitude of these forces. Round to two decimal places in all intermediate steps and in your final answer.

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  1. 9 September, 18:41
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    Given:

    100 lbs at 50°

    50 lbs at 160°

    1st vector:

    100 lbs cos (50°) = 64.3 lbs ⇒ positive x direction

    100 lbs sin (50°) = 76.60 lbs ⇒ positive y direction

    2nd vector:

    50 lbs cos (160°) = - 46.98 lbs ⇒ negative x direction

    50 lbs sin (160°) = 17.10 lbs ⇒ positive y direction

    x values:

    64.3 lbs + (-46.98 lbs) = 17.32 positive x direction

    y values:

    76.60 lbs + 17.10 lbs = 93.70 positive y direction

    Use Pythagorean theorem to find the resultant.

    Positive y direction = long leg of the right triangle

    Positive x direction = short leg of the right triangle

    Resultant = hypotenuse of the right triangle

    a² + b² = c²

    93.70² + 17.32² = c²

    8779.69 + 299.98 = c²

    9079.67 = c²

    √9079.67 = √c²

    95.29 lbs = c

    Resultant is 95.29 lbs.

    Direction of the resultang.

    Θ = tan^-1 (93.7/17.32) = 79.53° above positive x axis.
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