Question

A system is made up of three bodies with respective velocities as follows: body A of mass 1.5 kg moving at 2.0 m/s, north; body B of mass 2.0 kg moving at 3.0 m/s, south; and body C of mass 5.2 kg moving at 2.5 m/s, northeast. What is the momentum of the system?

Answer 1

The momentum of the system can be expressed in vector form:

$$\vec{p}=\vec{p}_x+\vec{p}_y,$$

where we assume North as positive y and East as positive x:

$$\vec{p}_{Cx}=m_Cv_C\text{ cos}45°=13i,\\ \vec{p}_{Cy}=m_Cv_C\text{ sin}45°=13i,\\ \vec{p}_{Ay}=m_Av_A=3j,\\ \vec{p}_{By}=-m_Bv_B-6j.$$

The total momentum is

$$\vec{p}=\vec{p}_{Cx}+\vec{p}_{Ay}+\vec{p}_{By}=[26i-3j]\text{ kg}·\text{m/s}.$$