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Two balls are projected from the same point in directions inclined at 60 and 30 to the horizontal. If they attain the same maximum height, the ratio of their velocities of projection is : A) 1 : 1 B) 1 : 2 C) 1 : p 3 D) p 3 : 1
Dear student Given-θ1=30°θ2=60°# Formula-- Height-H = u^2.(sinθ)^2 / 2g- Range-R = u^2.sin2θ / g# Calculations-Let u1 and u2 be the initial velocities for angle 30° and angle 60°.a) When range is same,R1 = R2u1^2.sin60/g = u2^2.sin120/gu1^2×0.866 = u2^2×0.866u1 = u2u1/u2 = 1b) When heights are same,H1 = H2u1^2.(sin30)^2/2g = u2^2.(sin60)^2/2gu1^2×(0.5)^2 = u2^2×(0.866)^20.25×u1^2 = 0.75×u2^2u1^2 = 3×u2^2u1/u2 = √3
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