A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2: 2: 3 . The two pieces of equal masses fly off perpendicular to each other with a speed of 18 ~m / s each. The velocity of the heavier fragment is _ _ _ _ m / s .

Step-by-step solution

From mass ratio 2:2:3 with total mass 14 kg: individual masses are 4 kg, 4 kg, and 6 kg. Setting coordinate axes along the motion directions of the two equal fragments: fragment 1 has momentum p₁ = 4 18 i = 72 i kg⋅m/s, and fragment 2 has p₂ = 4 18 j = 72 j kg⋅m/s. By momentum conservation, initially at rest: p₁ + p₂ + p₃ = 0 , so p₃ = -72 i - 72 j kg⋅m/s. Velocity of 6 kg fragment: v₃ = p₃ 6 = -12 i - 12 j m/s. Speed: | v₃ | = 144 + 144 = 288 = 12 2 m/s.