The velocity of the third piece is 124.02 m/s at 1.05⁰ below the horizontal.
Velocity of the third piece
The velocity of the third piece is calculated from the principle of conservation of linear momentum.
mu = m₁u₁ + m₂u₂ + m₃u₃
where;
- m is mass of the clay
- u is velocity of the clay
- u₁ is velocity of first piece
- u₂ is velocity of second piece
- u₃ is velocity of third piece
- m₃ is mass of the third piece = 6 kg - (2 kg + 1 kg) = 3 kg
Momentum in y - direction
6(22)sin(0) = 2(10)sin32 - 1(8)sin(28) + 3u₃y
0 = 6.84 + 3u₃y
u₃y = -6.84/3
u₃y = -2.28 m/s
Change in momentum
ΔP = Pf - Pi = J
where;
- Pf is final momentum
- Pi is the initial momentum
- J is impulse
2640(0.1) = 2(10)cos32 + 1(8)cos(28) + 3u₃x - 6(22)
264 = -108 + 3u₃x
3u₃x = 372
u₃x = 372/3
u₃x = 124 m/s
Resultant velocity
u₃ = √(124² + 2.28²)
u₃ = 124.02 m/s
Direction of the velocity
tanθ = u₃y/u₃x
tanθ = 2.28/124
tanθ = 0.018
θ = 1.05⁰ (below the horizontal)
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