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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 = 13sin θB13 will I get the same answer? Check]
If θ1 = 60 & θ2 = 30
Then sin60sin30 = 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
= 4sin120sin60
= 4sin(180120)sin60
sinθ = sin(π - θ)
= 4.


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