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What is the relation between Kinetic Energy and Max.Heights?
How to solve these kind of problems;-
Ratio of min.Kinetic energies of two projectiles of same mass is 4:1.REatio of Max.height attained by them is also 4:1.Ratio of their ranges would be?
a)16:1 b)4:1 c)8:1 d)2:1
Plz explain this elaborately.
The kinetic energies are minimum at the maximum height where velocity is ucosx
Hence 1/2 mu^2cos^2x1= 4*1/2 mv^2cos^2x2
or, ucosx1 = 2vcosx2........(1)
Maximum height is given by H = u^2sin^x/2g
Hence u^2sin^2x1/2g = 4*v^2sin^2x2/2g
or, usinx1 = 2vsinx2.......(2)
(2)/(1) gives tanx1=tanx2 or x1=x2
Using in (1) we get ucosx1 = 2vcosx1
hence u=2v
Therefore R1/R2 = {u^2sin2x1/g}/{v^2sin2x2/g} = (2v)^2sin2x1/v^2sin2x2 = 4
Hence option B is correct.
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