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Two bodies are placed at a distance 4 km and 6·5 km from the gun. When the bullet is fired at an angle of 30° with horizontal, it hits the body at 4 km. At what angle the bullet should be fired so that it may hit the second body?

Horizontal range is given by, 

                       straight R equals fraction numerator straight u squared sin space 2 straight theta over denominator straight g end fraction

Therefore the ratio of horizontal ranges R1 and R2 for angles of projections θ1 and θ2 is,

                 space space straight R subscript 1 over straight R subscript 2 equals fraction numerator sin space 2 straight theta subscript 1 over denominator sin space 2 straight theta subscript 2 end fraction

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We have here,

Angle space of space projection comma space straight theta subscript 1 equals 30 degree

Horizontal space range comma space straight R subscript 1 space equals space 4 space km

Horizontal space range comma space straight R subscript 2 equals 6.5 space km

Therefore, 

sin 2 straight theta subscript 2 equals sin 60 degree cross times fraction numerator 6.5 over denominator 4 end fraction equals 1.407 greater than 1, which is not possible.

Therefore for same speed of bullet, the bullet can not hit the body at a distance of 6·5km.

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