A plate falls vertically to the floor and breaks up into three pieces, which slide 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 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

Conservation of momentum can be used to solve this problem, as the total momentum before the impact is zero (since the plate was falling vertically) and the total momentum after the impact is also zero (since the pieces are moving in different directions). 
Let the velocity of the third piece be (vx, vy). Then we have:
320g(2.00 m/s) + 355g(0 m/s) + 100g(vx, vy) = 0

Solving for vx and vy, we get:
vx ≈ -0.94 m/s
vy ≈ -0.74 m/s

The direction of the third piece's velocity is given by:
θ = tan⁻¹(vy/vx) = tan⁻¹(0.74/0.94) ≈ 39.8° from the x-axis, which is closest to answer choice B.

A Plate Falls Vertically to the Floor and Breaks Up