A stone projected with a velocity u at an angle θ θ with the horizontal reaches maximum height H 1 . When it is projected with velocity u at an angle \(\left(\frac{\pi}{2} - \theta \right)\) with the horizontal, it reaches maximum height H 2 . The relation between the horizontal range R of the projectile, H 1 and H 2 is
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\(H_1 = \frac{u^2 \sin^2 \theta}{2g}\) and \(H_2 = \frac{u^2 \sin^2(90 - \theta)}{2g} = \frac{u^2 \cos^2 \theta}{2g}\)
\(H_1 H_2 = \frac{u^2 \sin^2 \theta}{2g} \times \frac{u^2 \cos^2 \theta}{2g} = \frac{(u^2 \sin 2\theta)^2}{16 g^2} = \frac{R^2}{16}\)
∴ ∴ \(R = 4 \sqrt{H_1 H_2}\)
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