Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h1 and h2. Which of the following is correct ?

Engineering

Physics

Projectile Motion

Question

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h₁ and h₂. Which of the following is correct ?

R²= 2 h₁h₂

R² = 4 h₁h₂

R² = 16 h₁h₂

R² = h₁h₂

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Angle of projections must be

θ, (90 – θ)

$h_{1} = \frac{u^{2} \sin^{2} θ}{2 g}, h_{2} = \frac{u^{2} \cos^{2} θ}{2 g}$

$R = \frac{2 u^{2} sinθcosθ}{g}$

$h_{1} h_{2} = \frac{u^{4} \sin^{2} {θcos}^{2} θ}{4 g^{2}}$

$R^{2} = \frac{4 u^{4} \sin^{2} {θcos}^{2} θ}{g^{2}}$

R² = 16h₁h₂