Explanation:
Let the speeds of father and son are [tex]v_f\ and\ v_s[/tex]. The kinetic energies of father and son are [tex]K_f\ and\ K_s[/tex]. The mass of father and son are [tex]m_f\ and\ m_s[/tex]
(a) According to given conditions, [tex]K_f=\dfrac{1}{3}K_s[/tex]
And [tex]m_s=\dfrac{1}{4}m_f[/tex]
Kinetic energy of father is given by :
[tex]K_f=\dfrac{1}{2}m_fv_f^2[/tex].............(1)
Kinetic energy of son is given by :
[tex]K_s=\dfrac{1}{2}m_sv_s^2[/tex]...........(2)
From equation (1), (2) we get :
[tex]\dfrac{v_f^2}{v_s^2}=\dfrac{1}{12}[/tex]..............(3)
If the speed of father is speed up by 1.5 m/s, so the ratio of kinetic energies is given by :
[tex]\dfrac{K_f}{K_s}=\dfrac{1/2m_f(v_f+1.5)^2}{1/2m_sv_s^2}[/tex]
[tex]v_s^2=4(v_f+1.5)^2[/tex]
Using equation (3) in above equation, we get :
[tex]v_f=\dfrac{1.5}{\sqrt3-1}=2.04\ m/s[/tex]
(b) Put the value of [tex]v_f[/tex] in equation (3) as :
[tex]v_s=7.09\ m/s[/tex]
Hence, this is the required solution.
