Question

Two particles A & B are projected with same speed so that the ratio of their maximum height reached is 3:1. If the speed of A is doubled without altering other parameters, the ratio of their horizontal ranges is

A

1:1

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B

2:1

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C

4:1

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D

3:2

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Solution

The correct option is C 4:1 From the question, u1 = u2 = u(say) We know already, H = u2sin2θ2g Let angles at which both are projected be θA & θB HA = u2sin2θA2g, HB = u2sin2θB2g Given, HAHB = 31{Let HA > HB} u2sin2θAu2sin2θB = 31 sinθAsinθB = √31 [can I assume sin θA = 1√3sin θB13 will I get the same answer? Check] If θ1 = 60∘ & θ2 = 30∘ Then sin60∘sin30∘ = √3212 = √3 So the angles are 60∘ = θ1,30∘ = θ2 Now u1 = 2u And we know, R = u2sin2θg RARB = ((2u)2sin2θA)1g(u2sin2θB)1g = sin2θA4sin2θA = 4sin120∘sin60∘ = 4sin(180∘−120∘)sin60∘ ∴ sinθ = sin(π - θ) = 4.

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