Now, lets see one more application of the formulas developed in the previous article.

Most of you must have come across the problem
Two projectiles have the same range R and heights H₁ & H₂ . Prove that
 R = 4 H₁H₂

Those of you who haven't solved this before try to do it. After you have broken your heads, or managed to solve it, come and see this solution.

As the ranges are same, they are projected at say, and 90 -

4H₁ = Rtan
4H₂ = Rtan(90-) => 4H₂ = Rcot
then,
16H₁H₂ = R²
R = 4 H₁H₂