JEE Main Physics question
Three guns are aimed at the centre of a circle. They are mounted on the circle, 120° apart, and fire in a timed sequence such that the three bullets collide at the centre and merge into a stationary lump. Two of the bullets have identical masses of 4.5 g with speeds v₁ and v₂; the third bullet has a mass of 2.5 g and speed 360 ms⁻¹. Find the unknown speeds v₁ and v₂. [AMU 2007]
Solution
Since the three guns point radially inward from positions 120° apart on the circle, the three bullets' momentum vectors are also directed 120° apart. For the resultant to vanish (so the merged lump is stationary), the vector sum of any two momenta must exactly cancel the third. By symmetry this requires the two
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