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Question

Two guns A and B can fire bullets at speed of 3 km/s and 4 km/s respectively. , They are fired in all possible directions, from a point on the horizontal ground. The ratio of maximum area covered by the fired bullets on the ground will be:

A
34
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B
916
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C
81256
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D
1
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Solution

The correct option is C 81256

When the guns fire bullets at some angle θ,it will follow the prabolic path for a projectile.
Range of the projectile is given by:
R=u2sin2θg.......(1)
Maximum area of fired bullets will correspond to area of circle with radius equal to maximum range (r=Rmax).
Range will be maximum for sin2θ=1 i.e θ=45
i.e,Rmax=u2g

Ratio of maximum area;
(Maximum Area)A(Maximum Area)B=π(Rmax)2Aπ(Rmax)2B=u4Ag2u4Bg2=u4Au4B

(Maximum Area)A(Maximum Area)B=(3)4(4)4=81256

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