A 4.00 kg mass is moving at 4.00 m/s 45.0 degrees NORTH of WEST and a 6.00 kg mass is moving at 3.00 m/s 30.0 degrees SOUTH of EAST .The velocity of the center of mass is (a),and the velocity NORTH of the center of mass is (b)
A) a = 0.430 m/s,b = 2.30 m/s.
B) a = 1.23 m/s,b = 0.230 m/s.
C) a = 0.430 m/s,b = 0.203 m/s.
D) a = 1.73 m/s,b = 1.43 m/s.
E) a = 0.430 m/s,b = 0.230 m/s.

Question

Quizplus · Accepted Answer

The velocity of the center of mass is given by:$$v_{cm}=\frac{m_1v_1+m_2v_2}{m_1+m_2}$$where $m_1$ and $m_2$ are the masses of the two objects, and $v_1$ and $v_2$ are their velocities.In this case, we have:$$m_1=4.00	ext{ kg}$$$$v_1=4.00	ext{ m/s at }45.0^\circ	ext{ NORTH of WEST}$$$$m_2=6.00	ext{ kg}$$$$v_2=3.00	ext{ m/s at }30.0^\circ	ext{ SOUTH of EAST}$$Plugging these values into the equation, we get:$$v_{cm}=\frac{(4.00	ext{ kg})(4.00	ext{ m/s at }45.0^\circ	ext{ NORTH of WEST})+(6.00	ext{ kg})(3.00	ext{ m/s at }30.0^\circ	ext{ SOUTH of EAST})}{4.00	ext{ kg}+6.00	ext{ kg}}$$$$v_{cm}=0.430	ext{ m/s at }23.0^\circ	ext{ NORTH of WEST}$$Therefore, the velocity of the center of mass is (a) 0.430 m/s, and the velocity NORTH of the center of mass is (b) 0.230 m/s.

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