Angle of Banking

For a Vehicle taking turn on a Curved path, If It's velocity exceeds a certain value it may loose it's balace and skid due to a force called Centrifugal Force.To Avoid this it should be provided by necessary centripetal force. It is done by slightly rising outer edge of the road. This is known as banking of roads. The angle made by the surface of road with horizontal direction is known as angle of banking.For a Vehicle moving with a velocity 'V' on a curved path of radious 'R', the angle of banking 'θ' and Velocity of vehicle are Related as:

θ=tan-1(	v2	)
	rg

Projectile Motion

Equation of motion of Projectile:
y = xtanθ - $ gx^2 # _2u^2cos^2θ

Note: Equation of the Projectile motion is Similar to the Equation of parabola, y=ax-bx² where a=tanθ and b = $g # _2u^2cos^2θ

Maximum Height Attained by a Projectile:
H = $2uSinθ # _g

Range or Displacement of Projectile:
R = $ u^2Sin2θ # _g

For given angles θ~^1 and θ~^2 , if θ~^1+θ~^2 = 90° then R~^1 = R~^2

Focal Length, Radious, Magnification, Power of Lenses

Convex Lense(Converging Lense) - Surfaces are Convex towards rarer medium.
Concave Lense(Diverging Lense) - Surfaces are Concave towards rarer medium

Focal Length of Lenses

1) f = $R~^1 R~^2 #_ (n-1)(R~^2 +R~^1 )

R - Radii of curvatures n - Refractive Index of Lense

2) f = $uv #_u+v

u - Object Distance. v - Image Dist.

Note: If given lense is equiconvex lense, then
R~^1 = R~^2 = R and f = $R#_2(n-1)
$ => n = 1 + $R #_2f