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a body projected vertically up travels a height h in the nth second.the distance travelled by it in next seconds

a body projected vertically up travels a height h in the nth second.the distance travelled by it in next seconds

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
As one of derived Newton's formulae:
velocity at the start of nth second= v=u-g(n-1)
h=ut-gt2/2
=>h=(u-g(n-1))2-g/2
=>u=√(h+g/2) + g(n-1) (this is the initial velocity i.e the speed at which the ball was thrown)
Speed at the end of n seconds= Vn=u-gn
=√(h+g/2) – g
Velocity after n seconds after the ball had travelled for n seconds = vn= u – gn-gn=u-2gn
Distance it will travel in the next n seconds = S
=>Vn2-vn2 = 2gS
=>S= ((u-gn)2-(u-2gn)2)/2g
=>S=(2un-3gn2)/2
=>S=((2√(h+g/2) + g(n-1))n-3gn2)/2 m
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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