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 velocity u2=ngb2 / 2h
5)
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) = 2xyz8) 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.
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