Respuesta :
Answer:
The speed of the center of mass is [tex](20.08\hat i+4.74 \hat j)m/s[/tex]
Explanation:
The speed of center of mass:
When a system of particles is moving, then the center of mass moves along with the system.
The center of mass velocity is ratio of the sum of momentum ( mass times velocity) to total mass of the system.
[tex]v_{cm}=\frac{v_1m_1+v_2m_2+......+v_nm_n}{m_1+m_2+......+m_n}[/tex]
Given that,
A 3.13 kg particle has a velocity [tex]a\hat i +b\hat j[/tex], where a= 24.2 m/s and b=1.35 m/s
and other particle has a velocity [tex]c\hat i+ d\hat j[/tex], where c= 1.27 m/s and d=8.54 m/s
Here, [tex]v_1 = 24.2 \hat i +1.35 \hat j[/tex] , [tex]m_1[/tex] = 3.13 kg
[tex]v_2 = 1.27 \hat i +8.54\hat j[/tex] , [tex]m_2[/tex] = 2.81 kg
The speed of the center of mass is
[tex]v_{cm}=\frac{v_1m_1+v_2m_2}{m_1+m_2}[/tex]
[tex]=\frac{(24.2 \hat i +1.35 \hat j) .3.13+( 1.27 \hat i +8.54\hat j). 2.81}{3.13+2.82}[/tex]
[tex]=\frac{(75.746\hat i +4.2255\hat j) +( 3.5687\hat i +23.9974\hat j)}{5.95}[/tex]
[tex]=20.08\hat i+4.74 \hat j[/tex] m/s
