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11 November, 04:17

A sailboat has a mass of 1.50*10^3 kg and is acted on by a force of 2.00*103 N toward the east, while the wind acts behind the sails with a force of 3.00*10^3 N in a direction 45° north of east. Find the magnitude and direction of the resulting acceleration.

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  1. 11 November, 07:24
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    Acceleration is 3.09 m/s²

    The direction of the acceleration is

    N 62.742° E

    Explanation:

    A sailboat has a mass of 1.50*10^3 kg and a force of 2.00*10^3 N is

    acting on it toward the east.

    The wind with force of 3.00*10^3N

    In a direction 45° north of east act on it.

    The resultant force is

    C² = A² + B² - 2ABCosc

    C² = 2² + 3² - 2 (2) (3) cos135

    C² = 4 + 9 + 8.485

    C² = 13+8.485

    C² = 21.485

    C = 4.635 * 10^3 N

    Let sinb = x

    3/x = 4.635/sin135

    3/x = 6.555

    X = 3/6.555

    X = 0.458

    But x = sin b

    b = sin^-1 0.458

    b = 27.258°

    90 - 27.258 = 62.742°

    The direction of the force is

    N 62.742° E

    Acceleration is F/m

    a = 4.635 * 10^3/1.50*10^3

    a = 3.09 m/s²
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