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Math Help - Rock's Ratio

  1. #1
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    Rock's Ratio

    A 4.0-kilogram rock and a 1.0-kilogram stone fall freely from rest from a height of 100 meters. After they fall for 2.0 seconds, the ratio of the rock’s speed to the stone’s speed is

    (1) 1:1 (3) 2:1
    (2) 1:2 (4) 4:1
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  2. #2
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    Quote Originally Posted by symmetry View Post
    A 4.0-kilogram rock and a 1.0-kilogram stone fall freely from rest from a height of 100 meters. After they fall for 2.0 seconds, the ratio of the rock’s speed to the stone’s speed is

    (1) 1:1 (3) 2:1
    (2) 1:2 (4) 4:1
    If I'm not mistaken, the free fall is v = g*t, where g = 9.8 m/s/s, thus we'll round to 10.

    It has nothing to do with the weight of the object, and thus they both fall at the same velocity. Therefore, the answer is (1).

    Objects that are in free-fall move under the influence of gravity alone; they do not experience air-resistance. More massive objects will not fall faster, unless there is a significant amount of air resistance. In summary, all objects that are in free-fall will have the same rate of acceleration, regardless of taking their mass into account. Topsquark can probably elaborate far more than I can on this physics question.
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  3. #3
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    Quote Originally Posted by symmetry View Post
    A 4.0-kilogram rock and a 1.0-kilogram stone fall freely from rest from a height of 100 meters. After they fall for 2.0 seconds, the ratio of the rock’s speed to the stone’s speed is

    (1) 1:1 (3) 2:1
    (2) 1:2 (4) 4:1
    Galileo's observation is that if air resistence is ignored, objects of differing mass fall near the Earth's surface equal distances in the same time, so at any time in a the fall the objects have the same speed.

    So the answer is 1:1

    RonL
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  4. #4
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    ok

    So, two objects of different mass falling to earth at the same time is possible if air resistance is applied.

    Very interesting concept.
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    Quote Originally Posted by symmetry View Post
    So, two objects of different mass falling to earth at the same time is possible if air resistance is applied.

    Very interesting concept.
    If air resistance is NOT applied!

    Therefore, in a vacuum they would fall at the same speed as the mass of the object does not matter.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by anthmoo View Post
    If air resistance is NOT applied!

    Therefore, in a vacuum they would fall at the same speed as the mass of the object does not matter.
    I once saw a feather in a vacuum fall alongside a rock. They DID fall at the same rate all the way down. It was kind of eerie actually.

    -Dan
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