A particle is projected with speed u such that its horizontal range is three times the maximum height attained. If the horizontal range is written as nu²/(25g), the value of n is:
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Question

A particle is projected with speed u such that its horizontal range is three times the maximum height attained. If the horizontal range is written as nu²/(25g), the value of n is:

G1 Physics · Accepted Answer

For projectile motion, R = u²sin2θ/g and H = u²sin²θ/(2g). Given, R = 3H. Therefore, u²(2sinθcosθ)/g = 3u²sin²θ/(2g). Cancel u²/g and one sinθ: 2cosθ = (3/2)sinθ ⇒ 4cosθ = 3sinθ ⇒ tanθ = 4/3. Hence, sinθ = 4/5, cosθ = 3/5. Therefore, R = u²(2sinθcosθ)/g = u²[2×(4/5)×(3/5)]/g = 24u²/(25g). Thus n = 24. Correct option: B.