# The range of R projectile is same when its maximum heights are h1 and h2. What is the relation between R1, h1, h2 ?

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

H1/R = tan Ф1 / 4 tan Ф1 = 4 H1 / R

R is same for Ф1 and 90-Ф1

H1 = u² sin² Ф1 / 2 g

H2 = u² sin² (90-Ф1) / 2 g = u² cos² Ф1 / 2 g

H1 + H2 = u²/2g

H1/H2 = tan² Ф1 = 16 H1²/R²

*R² = 16 H1 H2*

H1/R = tan Ф1 / 4 tan Ф1 = 4 H1 / R

R is same for Ф1 and 90-Ф1

H1 = u² sin² Ф1 / 2 g

H2 = u² sin² (90-Ф1) / 2 g = u² cos² Ф1 / 2 g

H1 + H2 = u²/2g

H1/H2 = tan² Ф1 = 16 H1²/R²