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) $39.9 ^ { \circ } \text { from the } + x \text {-axis }$
B) $216.9 ^ { \circ } \text { from the } + x \text {-axis }$
C) $219.8 ^ { \circ } \text { from the } + x \text {-axis }$
D) $36.9 ^ { \circ } \text { from the } + x \text {-axis }$
E) $39.8 ^ { \circ } \text { from the } + x \text {-axis }$

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 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) $39.9 ^ { \circ } \text { from the } + x \text {-axis }$
B) $216.9 ^ { \circ } \text { from the } + x \text {-axis }$
C) $219.8 ^ { \circ } \text { from the } + x \text {-axis }$
D) $36.9 ^ { \circ } \text { from the } + x \text {-axis }$
E) $39.8 ^ { \circ } \text { from the } + x \text {-axis }$

Quizplus · Accepted Answer

The conservation of momentum in the x and y directions must be applied. The total momentum before the break is zero, so the sum of the momenta of the pieces must also be zero. Solving for the third piece's velocity components and using trigonometry gives the direction as $219.8 ^{\circ}$ from the +x-axis.

A Dinner Plate Falls Vertically to the Floor and Breaks 39.9∘ from the +x-axis 39.9 ^ { \circ } \text { from the } + x \text {-axis }39.9∘ from the +x-axis

A Dinner Plate Falls Vertically to the Floor and Breaks $39.9 ^ { \circ } \text { from the } + x \text {-axis }$