A 8.00 kg mass is moving at 5.00 m/s SOUTH and a 6.00 kg mass is moving at 7.00 m/s EAST.The velocity of the center of mass is (a),and the velocity NORTH of the center of mass is (b)
A) a = +40.0 m/s,b = +3.00 m/s.
B) a = +3.00 m/s,b = +40.0 m/s.
C) a = -3.00 m/s,b = -3.00 m/s.
D) a = +3.00 m/s,b = -40.0 m/s.
E) a = +40.0 m/s,b = -40.0 m/s.

Question

Quizplus · Accepted Answer

We can use the equations for the center of mass:
xcm = (m1x1 + m2x2)/M
ycm = (m1y1 + m2y2)/M
where m1 and m2 are the masses, x1 and y1 are the velocities in the x and y directions for the 8.00 kg mass, x2 and y2 are the velocities in the x and y directions for the 6.00 kg mass, and M = m1 + m2.

Plugging in the given values, we get:
xcm = (8.00 kg)(0 m/s) + (6.00 kg)(7.00 m/s)/14.00 kg = 21.00 m/s EAST
ycm = (8.00 kg)(-5.00 m/s) + (6.00 kg)(0 m/s)/14.00 kg = -3.57 m/s SOUTH

Therefore, the velocity of the center of mass is +21.00 m/s EAST and the velocity NORTH of the center of mass is -3.57 m/s, which is closest to choice D.

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