Aplate 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? you can neglect any horizontal forces during the crash.36.9° from the x-axis

Refer to the diagram shown below.

Define the (x,y) plane as the horizontal plane of the floor.
There was no momentum in the (x,y) plane before the plate hit the floor.

Let the velocity components in the (x) and (y) directions of the 100 g mass be Vx and Vy respectively, and that the resultant velocity, V, makes an angle θ below the negative x-axis as shown.

Because momentum is conserved, therefore
100*Vx + 320*2 = 0
100Vx = -640
Vx = -6.4 m/s

100Vy + 355*1.5 = 0
100Vy = -532.5
Vy = -5.325 m/s

V = √[(-6.4)² + (-5.325)²] = 8.33 m/s
θ = tan⁻¹ (-5.325/-6.4) = 39.8°

The direction is 39.8° below the negative x-axis
The speed is 8.33 m/s

As newton's first law states a object in motion stays in motion