Question

A projectile has the same range R when the maximum height attained by it either H₁ or H₂. 
Find relationship between R, H₁ and H₂.

Answer 1

R = u² sin 2Ф1 / g = u² sin (180 - 2Ф1) / g = u² sin 2(90-Ф1) /g

R is same for Ф1 and 90-Ф1.

H1 = R tanФ1 /4

H2 = R tan (90-Ф1) /4 = R /4 tanФ1

H1 H2 = R² / 16