Question

A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. Immediately after the impact, a 320 g piece moves alone the +x axis with a speed of 2.00 m/s and a 355 g piece moves along the +y axis with a speed of 1.50 m/s. The third piece has a mass of 100g. In what direction relative to the +x axis does the third piece move?

Answer 1

Mass of the first plate m₁ = 320g = 0.32 kg

Mass of the second plate m₂ = 355 g = 0.355 kg

Velocity of the first plate v₁ = 2.0 m/s i

Velocity of the second plate v₂ = 1.50 m/s j

Mass of the third plate m3 = 100 g = 0.1 kg

From law of conservation of momentum

along x-axis

                  m₁v₁ + m₃v₃ = 0

the velocity of mass m3 along axis

                       v₃ = - m₁v₁/m₃ = - (0.32 kg)(2.0 m/s) / 0.1 kg

                                                 =- 6.4 m/s i

alon y-axis

                 m₂v₂ + m₃v₃

then velocity of mass along y-axis

                                            v₃ = - m₂v₂/m₃

    = - (0.355 kg)(1.5 m/s) / 0.1 kg

                                                =- 5.325 m/s i

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Therefore the speed of third mass

                        v₃ = ?(6.4m/s)² + (5.325 m/s)²

                             = 8.32 m/s

and the angle   ? = tan-1(5.325 /6.4)

                           = 39.76

Since both component in negative axis then

Therefore the angle ? = 180 +39.76 = 219.76 deg from +x-axis.