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saket_brutus (112)

Cool goIITian

total posts: 49
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Hi,

I have a few that u guys may already know. Here goes :-

1) loss of energy in an inelastic collision

= [m₁m₂ (v₁-v₂)²(1-e)²] / 2(m₁+m₂)

2) fraction of KE transferred in an elastic collision where ,m₁=m; m₂=xm

=4x / (1+x)²

3) if a bullet or any body loses f fraction of velocity after every collision with a plank, then no. of planks required to stop the bullet=1 / (1-(1-f)²)

4) a body is projected from a step (stair has 'n' steps) of height 'h'and breadth 'b'. if the body hits the nth step, then square of projection velocityu²=ngb²/ 2h

dx / x(1+xⁿ) = (1/n) log(xⁿ/1+xⁿ) +c

6) IF cos^-1x + cos^-1y + cos^-1z=pi, then x²+y²+z²+2xyz = 1

7) IF sin^-1x + sin^-1y + sin^-1z=pi, then x(1-x²)+y(1-y²)+z(1-z²) = 2xyz

8) IF tan^-1x + tan^-1y + tan^-1z=pi, then x+y+z=xyz

9) tan^-1(x/y) + tan^-1(y-x / y+x) = pi/4

10) IF tan^-1x + tan^-1y =pi/2 or cot^-1x + cot^-1y = pi/2, then xy=1

Cheers.

Saket

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