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 along 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 100 g.In what direction relative to the +x-axis does the third piece move?
A)216.9° from the +x-axis
B)219.8° from the +x-axis
C)36.9° from the +x-axis
D)39.9° from the +x-axis
E)39.8° from the +x-axis

Question

Quizplus · Accepted Answer

To find the direction of the third piece, we use the conservation of momentum. The total momentum before the plate breaks is zero (since it was falling vertically and we're only considering horizontal momentum). Thus, the vector sum of the momenta of the three pieces after the break must also be zero. The momentum of the first piece is $0.320 \, \text{kg} \times 2.00 \, \text{m/s}$ in the +x direction, and the momentum of the second piece is $0.355 \, \text{kg} \times 1.50 \, \text{m/s}$ in the +y direction. The third piece must have a momentum that, when added vectorially to these, results in zero total momentum. By calculating the angle of this vector (which represents the third piece's momentum direction) with respect to the +x-axis, we find it to be 219.8°, taking into account the direction and magnitude of the momenta of the first two pieces.

A Dinner Plate Falls Vertically to the Floor and Breaks