Question

I need help with this question There is 4 answersa)b)c)d)

Answer 1

Given,

The velocity of the joggers, v=-3.50 m/s

The mass of Jim, M=100 kg

The mass of Tom, m=59 kg

(a) The kinetic energy of the system is given by,

`\begin{gathered} E_a=(1)/(2)mv^2+(1)/(2)Mv^2 \\ =(1)/(2)v^2(m+M) \end{gathered}`

On substituting the known values,

`\begin{gathered} E_a=(1)/(2)*3.50^2(59.0+100) \\ =973.88\text{ J} \end{gathered}`

Thus the kinetic energy of the system is 973.88 J

(b)

The total momentum of the system is given by,

`\begin{gathered} p_b=mv+Mv \\ =(m+M)v \end{gathered}`

On substituting the known values,

`\begin{gathered} p_b=(59+100)*3.50 \\ =556.5\text{ kg}\cdot\text{ m/s} \end{gathered}`

Thus the total momentum of the system is 556.5 kg m/s

(c)

Given that the velocity of Tom is -v

The total kinetic energy of the system is given by,

`\begin{gathered} E_c=(1)/(2)Mv^2+(1)/(2)m(-v)^2 \\ =(1)/(2)(Mv^2+m(-v)^2) \end{gathered}`

On substituting the known values,

`\begin{gathered} E_c=(1)/(2)(100*3.50^2+59*(-3.50)^2) \\ =973.88\text{ J} \end{gathered}`

Thus the total kinetic energy of the system, in this case, is 973.88 J

(d)

The total momentum of the system is given by,

`\begin{gathered} p_d=Mv+m(-v) \\ =v(M-m) \end{gathered}`

On substituting the known values,

`\begin{gathered} p_d=3.50(100-59) \\ =143.5\text{ kg}\cdot\text{ m/s} \end{gathered}`

Thus the total momentum of the system, in this case, is 143.5 kg m/s