Respuesta :
(a). Give data:
* The mass of the marble A is m1 = 0.08 kg
* The mass of marble B is m2 = 0.05 kg
* The initial velocity of m1 is u1 = 0.5 m/s
* The initial velocity of m2 is u2 = 0 m/s
* The final velocity of m1 is v1 = -0.1 m/s
According to the law of conservation of momentum,
[tex]\begin{gathered} m_1u_1+m_2u_2=m_1v_1+m_2v_2 \\ m_1u_1+m_2u_2-m_1v_1=m_2v_2 \\ \frac{(m_1u_1+m_2u_2-m_1v_1)}{m_2}=v_2 \end{gathered}[/tex]where v2 is the final velocity of the marble B,
Substituting the known values,
[tex]\begin{gathered} \frac{(0.08\times0.5)+(0.05\times0)-(0.08\times(-0.1))}{0.05}=_{}v_{_2} \\ \frac{0.04+0+0.008}{0.05}=v_2_{}_{}_{} \\ \frac{0.04+0.008}{0.05}=v_2 \\ \frac{0.048}{0.05}=v_2 \end{gathered}[/tex]Thus, the final velocity of the marble B is,
[tex]\begin{gathered} v_2=\frac{0.048}{0.05} \\ v_2=0.96ms^{-1} \end{gathered}[/tex]Thus, the value of the velocity of the marble B is 0.96 meters per second.
(b). The multiplication of terms 0.08 and -0.1 is,
The term 0.08 can be written as,
[tex]0.08=\frac{8}{100}[/tex]The term -0.1 can be written as,
[tex]-0.1=\frac{-1}{10}[/tex]Thus, the multiplication of 0.08 with -0.1 is,
[tex]\begin{gathered} 0.08\times(-0.1)=\frac{8}{100}\times(-\frac{1}{10}) \\ =-(\frac{8}{100}\times\frac{1}{10}) \\ =-\frac{8}{1000} \\ =-0.008 \end{gathered}[/tex]Thus, the multiplication of 0.08 with -0.1 is -0.008.
