Objects A, B, and Care moving as shown in Fig. E8.3.Find the x- and y-components of the net momentum of the particlesif we define the system to consist of (a) Aand C, (b) Band C,(c) all three objects.

From the figure we can observe that,

Mass of the object A, $m_A=5.0kg$

Velocity of object A,$v_A=v_{Ay}=-11\mathrm{m}/\mathrm{s}$

Mass of the object B,$m_B=6.0\mathrm{kg}$

Velocity and angle of the object B, ${\mathrm{v}}_{\mathrm{B}}=10.0\mathrm{m}/\mathrm{s},\mathrm{\theta }=60°$

Mass of the object C,$m_C=10\mathrm{kg}$

Velocity of the object C,$v_C=v_{Cx}=-3.0m/s$$v_C=v_{Cx}=-3.0\mathrm{m}/\mathrm{s}$

A property of a moving body resulting from its mass and motion that is roughly equivalent to the product of its mass and velocity: a property of a moving body that determines how long it will take for it to come to rest when applied to a constant force.

As we know the momentum of an object is

$\overrightarrow{p}=m\overrightarrow{v}$

If $p_x$is x component of momentum and $p_y$is y component of momentum

Then

$p_x+p_y=m{\overrightarrow{v}}_x+m{\overrightarrow{v}}_y$

Therefore,

The x-component of the net momentum of the system consists of A and C can be given as.

$$\begin{gathered} p_{Ax}+p_{Cx}=m_A{v}_{Ax}+m_c{v}_{cx} \\ =50\mathrm{kg}\left(0\right)+10\mathrm{kg}-\left(-3\mathrm{m}/\mathrm{s}\right) \\ =-30\mathrm{kg}.\mathrm{m}/\mathrm{s} \end{gathered}$$

The x component of the net momentum of the system consists of A and C is -30kg.m/s.

The y component of the net momentum of the system consists of A and C can be given as.

$$\begin{gathered} p_{Ax}+p_{Cx}=m_A{v}_{Ay}+m_c{v}_{cy} \\ =5\mathrm{kg}\left(-11\mathrm{m}/\mathrm{s}\right)+10\mathrm{kg}\left(0\right) \\ =-55.0\mathrm{kg}.\mathrm{m}/\mathrm{s} \end{gathered}$$

The y component of the initial momentum of the system consists of A and C is -55.0kg/m/s

Given in the question.

Mass of the object B,$m_B=6.0\mathrm{kg}$

Velocity and angle of the object B,$v_B=10.0\mathrm{m}/\mathrm{s},\mathrm{\theta }=60°$

Therefore,

X-component of the velocity of object B, $v_{Bx}=10.0\cos 60\mathrm{m}/\mathrm{s}$

Y-component of velocity of the object B,$v_{By}=10.0\sin 60\mathrm{m}/\mathrm{s}$

Mass of object C,$m_C=10kg$

Velocity of object$v_C=v_{cx}=-3.0\mathrm{m}/\mathrm{s}$

The x component of the net momentum of the system consists of B and C can be given as.

$$\begin{gathered} p_{Bx}+p_{Cx}=m_B{v}_{Bx}+m_c{v}_{cx} \\ =6\mathrm{kg}\left(10\cos 60\mathrm{m}/\mathrm{s}\right)+10\mathrm{kg}\left(-3\mathrm{m}/\mathrm{s}\right) \\ =30\mathrm{kg}.\mathrm{m}/\mathrm{s}-30\mathrm{kg}.\mathrm{m}/\mathrm{s} \\ =0 \end{gathered}$$

The x component of the net momentum of the system consists of B and C is 0.

The y component of the net momentum of the system consists of B and C can be given as.

$$\begin{gathered} p_{By}+p_{Cy}=m_B{v}_{By}+m_c{v}_{cy} \\ =6\mathrm{kg}\left(10\cos 60\mathrm{m}/\mathrm{s}\right)+10\mathrm{kg}\left(0\right) \\ =52\mathrm{kg}.\mathrm{m}/\mathrm{s} \end{gathered}$$

The y component of the net momentum of the system consists of B and C is 52kg.m/s .

We know,

$$\begin{gathered} {\mathrm{m}}_{\mathrm{A}}=5.0\mathrm{kg} \\ {\mathrm{v}}_{\mathrm{A}}={\mathrm{v}}_{\mathrm{Ay}}=-11\mathrm{m}/\mathrm{s} \\ {\mathrm{m}}_{\mathrm{B}}=6.0\mathrm{kg} \\ {\mathrm{v}}_{\mathrm{Bx}}=10.0\cos 60\mathrm{m}/\mathrm{s} \\ {\mathrm{v}}_{\mathrm{By}}=10.0\sin 60\mathrm{m}/\mathrm{s} \\ {\mathrm{m}}_{\mathrm{C}}=10\mathrm{kg} \\ {\mathrm{v}}_{\mathrm{C}}={\mathrm{v}}_{\mathrm{Cx}}=-3.0\mathrm{m}/\mathrm{s} \end{gathered}$$

The x component of the net momentum of the system consists of A, B and C can be given as.

$$\begin{gathered} p_{Ax}+p_{Bx}+p_{Cx}=m_A{v}_{ax}+m_B{v}_{Bx} \\ =5\mathrm{kg}\left(0\right)+6\mathrm{kg}\left(10\cos 60\mathrm{m}/\mathrm{s}\right)+10\mathrm{kg}\left(-3\mathrm{m}/\mathrm{s}\right) \\ =30\mathrm{kg}.\mathrm{m}/\mathrm{s}-30\mathrm{kg}.\mathrm{m}/\mathrm{s} \\ =0 \end{gathered}$$

The x component of the net momentum of the system consists of A, B and C is 0 .

The y component of the net momentum of the system consists of A, B and C can be given as.

$$\begin{gathered} p_{Ay}+p_{By}+p_{Cy}=m_A{v}_{ay}+m_B{v}_{By} \\ =5\mathrm{kg}\left(-11\mathrm{m}/\mathrm{s}\right)+6\mathrm{kg}\left(10\sin 60\mathrm{m}/\mathrm{s}\right)+10\mathrm{kg}\left(0\right) \\ =\left(-55+52\right)\mathrm{kg}.\mathrm{m}/\mathrm{s} \\ =-3\mathrm{kg}.\mathrm{m}/\mathrm{s} \end{gathered}$$

The y component of the net momentum of the system consists of A, B and C is -3kg.m/s .