An explosion breaks a rock into three pieces moving in a horizontal plane. A 1 kg fragment moves at 12 m s⁻¹ and a 2 kg fragment moves at 8 m s⁻¹ in a perpendicular direction. The third fragment moves at 4 m s⁻¹. Find its mass.
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Question

An explosion breaks a rock into three pieces moving in a horizontal plane. A 1 kg fragment moves at 12 m s⁻¹ and a 2 kg fragment moves at 8 m s⁻¹ in a perpendicular direction. The third fragment moves at 4 m s⁻¹. Find its mass.

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G1 Physics · Accepted Answer

Initially the rock is at rest, so the vector momenta sum to zero. The first two momenta are perpendicular: p₁=1×12=12 and p₂=2×8=16 kg m s⁻¹. The third must have momentum magnitude √(12²+16²)=20. Thus m₃=20/4=5 kg. Answer: B.