Question

A stone projected with velocity u at an angle θ with the horizontal reaches maximum height H₁. When it is projected with velocity u at an angle ((π)/(2)-θ), it reaches maximum height H₂. The relation between the horizontal range R of the projectile, heights H₁ and H₂ is:

• A. \(R=4\sqrt{H_1H_2}\)
• B. \(R=4(H_1-H_2)\)
• C. \(R=4(H_1+H_2)\)
• D. R=(H₁²)/(H₂)

Hint:

Complementary angles give same range but different maximum heights.

Answer 1

The Correct Option is A

Step 1: Maximum heights: H₁=(u²sin²θ)/(2g), H₂=(u²cos²θ)/(2g)
Step 2: Horizontal range: R=(u²\sin2θ)/(g)
Step 3: Eliminating u and θ: R=4√(H₁H₂)