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

Complementary Angle Theorem

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For angles theta and (90 - theta):

  • R(theta) = u^2sin(2theta)/g
  • R(90-theta) = u^2sin(2(90-theta))/g = u^2sin(180-2theta)/g = u^2sin(2theta)/g

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

But heights differ:

  • H(theta) = u^2*sin^2(theta)/(2g)
  • H(90-theta) = u^2*cos^2(theta)/(2g)
  • Ratio: H(theta)/H(90-theta) = tan^2(theta)

And flight times differ:

  • T(theta) = 2u*sin(theta)/g
  • T(90-theta) = 2u*cos(theta)/g
  • Ratio: T(theta)/T(90-theta) = tan(theta)

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

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