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By which velocity a ball be projected vertically downward so that the distance covered by it in 5th second is twice the distance it covers in its 6th second (g=10m/s^2?
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By which velocity a ball be projected vertically downward so that the ...
Problem: Find the initial velocity of a ball projected vertically downwards so that the distance covered by it in the 5th second is twice the distance it covers in its 6th second, given that g=10m/s^2.

Solution:

Let the initial velocity of the ball be u.

Using the first equation of motion,
s = ut + 1/2 at^2

The distance covered by the ball in the 5th second is given by,
s5 = u(5) + 1/2 (10)(5)^2
s5 = 25u + 125

The distance covered by the ball in the 6th second is given by,
s6 = u(6) + 1/2 (10)(6)^2
s6 = 30u + 180

Given that s5 = 2s6
25u + 125 = 2(30u + 180)
25u + 125 = 60u + 360
35u = 235
u = 6.71 m/s (approx)

Therefore, the initial velocity of the ball should be 6.71 m/s (approx) for the distance covered by it in the 5th second to be twice the distance it covers in its 6th second.

Answer: The initial velocity of the ball should be 6.71 m/s (approx).
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By which velocity a ball be projected vertically downward so that the ...
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By which velocity a ball be projected vertically downward so that the distance covered by it in 5th second is twice the distance it covers in its 6th second (g=10m/s^2?
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