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?
Options

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?

G1 Physics · Accepted Answer

For the two equal-range trajectories, the launch angles are complementary: θ and 90° - θ. Their maximum heights are h₁ = u²sin²θ/(2g) and h₂ = u²cos²θ/(2g). Hence 16h₁h₂ = 4u⁴sin²θcos²θ/g² = u⁴sin²2θ/g² = R². Therefore R² = 16h₁h₂, option B.