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)