a body is falling from rest covered distances S1, S2, S3 in first second and third seco.ds of its fall. Calculate the ratio of S1, S2, and S3
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a body is falling from rest covered distances S1, S2, S3 in first second and third seco.ds of its fall. Calculate the ratio of S1, S2, and S3
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S = ut+(1/2)at² = (1/2)(10)t² = 5t²
S after 1 sec =5(1)²=5
S after 2 sec =5(2)²=20
S after 3 sec5(3)²=45
Distance covered in first second = S1
distance covered in 2nd sec = 20-5=15
distance covered in 3rd sec =45-20 =25
SO,
S1:S2:S3 = 1:15:25 = 1:3:5
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Let the body dropped from rest, so after seconds, the distance travelled is,
Since g, acceleration due to gravity, is a constant,
Hence the ratio of displacements measured from initial point attained after times is,
This is ratio of displacements measured from initial point. The ratio of displacements covered between consecutive times is,
Let
Assume and Then we get So,
In terms of
Also, from (1)
This ratio is known by the name "Galileo's Law of Odd Distances / Numbers".
The case is irrespective of initial velocity; the initial velocity need not be zero.
So the ratio of distances covered in first, second and third seconds of fall, is,