Question

An 150 kg object at rest explodes into three pieces. If one of the pieces is traveling at 15 m/s, another piece is traveling at 20 m/s 135° from the first piece, and the third piece is traveling 10 m/s at 225° from the first piece, what is the mass of the three pieces.

Answer 1

let the first piece is travelling along the positive X-axis

V_1x = 15 m/s           , V_1y = 0

V_2x = 20 Cos135 = - 14.14 m/s        ,       V_2y = 20 Sin135 = 14.14 m/s

V_3x = 10 Cos225 = - 7.1 m/s           ,           V_3y = 10 Sin225 = - 7.1 m/s

using conservation of momentum along X-direction

m₁ V_1x + m₂ V_2x + m₃ V_3x = 0

15 m₁ -14.14 m₂ - 7.1 m₃ = 0

15 m₁ = 14.14 m₂ + 7.1 m₃    eq-1

using conservation of momentum along Y-direction

m₁ V_1y + m₂ V_2y + m₃ V_3y = 0

0 m₁ +14.14 m₂ - 7.1 m₃ = 0

m₃ = 2 m₂ eq-2

also , m₁ + m₂ + m₃ = 150

using eq-2

m₁ + m₂ + 2 m₂ = 150

m₁ + 3 m₂ = 150

m₁ = 150 - 3 m₂ eq-3

using eq-1 , eq-2 and eq-3

15 m₁ = 14.14 m₂ + 7.1 m₃

15 (150 - 3 m₂ ) = 14.14 m₂ + 7.1 (2 m₂)

m₂ = 30.7 kg

m₁ = 150 - 3 m₂ = 150 - 3 (30.7) = 57.9 kg

m₃ = 2 m₂ = 2 x 30.7 = 61.4 kg