I dropped a 5kg plate straight down onto the ground and it shattered into three

Question

I dropped a 5kg plate straight down onto the ground and it shattered into three pieces. The pieces shot off into three different directions and slid across the ground until they came to a stop. The pieces of plate experience friction against the ground with coefficient of kinetic friction, k = .4. Call the point where I dropped the plate the origin, (x, y) = (0, 0). I found a 2kg piece at (x, y) = (3, 7), and a 1.2kg piece at (x, y) = (9, 4). Where did the third piece come a stop? Note all (x,y) positions are in meters

Explanation / Answer

The center of mass at a point on x-axis is given by,

xCM = m1 x1 + m2 x2 / (m1 + m2)

xCM = (2 kg) (3 m) + (1.2 kg) (-9 m) / [(2 kg) + (1.2 kg)]

xCM = - (4.8 kg.m) / (3.2 kg)

xCM = - 1.5 m

The center of mass at a point on y-axis is given by,

yCM = m1 y1 + m2 y2 / (m1 + m2)

yCM = (2 kg) (7 m) + (1.2 kg) (-4 m) / [(2 kg) + (1.2 kg)]

yCM = - (9.2 kg.m) / (3.2 kg)

yCM = - 2.87 m

The third piece come to stop at a distance (x, y) which is given as :

x = -1.5 m   and   y = -2.87 m

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