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    Please explain in details how to get the answers for problems below.

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    Problem 1:
    A box is sliding down a plane inclined at an angle of 20 degrees from the horizontal. Find the acceleration of the box, neglecting friction and air resistance.

    Possible answers:
    (1) 0.342 m^2g
    (2) 0.342 m
    (3) 0.342 g
    (4) 0.342 mg
    (5) 0.940 m^2g
    (6) 0.940 m
    (7) 0.940 g
    (8) 0.940 mg

    Problem 2:
    A box that is hurled up the inclined plane of the above Problem 1, starts up the plane with an initial velocity of 1,000 cm/sec. Find the speed of the box moving up the plane 3 sec later.

    Possible answers:
    (1) 0 cm/sec
    (2) -5.5 cm/sec
    (3) 8.9 cm/sec
    (4) 10.1 cm/sec
    (5) 42.5 cm/sec
    (6) 63.3 cm/sec
    (7) 75.3 cm/sec
    (8) 98.1 cm/sec.

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    Solution Preview

    For the first question, you must first draw a free body diagram very similar to this one:


    The force which moves the box, in that diagram, is mgx. This force can be represented via trigonomic relationships with the force of gravity (mg) itself:

    sin theta = mgx / mg

    In our case, our ...

    Solution Summary

    The solution finds the acceleration of the box, neglecting friction and air resistance. It also assists with drawing a free body diagram.