Part of JME-01 — Kinematics: Rectilinear & Projectile Motion

Complementary Angle Theorem

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For angles theta and (90 - theta):

  • R(theta) = u2u^2*sin2thetag\frac{2*theta}{g}
  • R(90-theta) = u2u^2sin(2(90-theta))/g = u2u^2*sin1802thetag\frac{180-2*theta}{g} = u2u^2*sin2thetag\frac{2*theta}{g}

Therefore R(theta) = R(90-theta).

But heights differ:

  • H(theta) = u2u^2*sin^2$$\frac{theta}{(2g)}
  • H(90-theta) = u2u^2*cos^2$$\frac{theta}{(2g)}
  • Ratio: HthetaH\frac{theta}{H}(90-theta) = tan2tan^2(theta)

And flight times differ:

  • T(theta) = 2u*sinthetag\frac{theta}{g}
  • T(90-theta) = 2u*costhetag\frac{theta}{g}
  • Ratio: TthetaT\frac{theta}{T}(90-theta) = tan(theta)

JEE favorite: RH relationship: R = 4H*cot(theta)

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