Answer:
[tex](a)0.5m(2v1v2+v2^{2})\\(b)0.5m(v2^{2}-v1^{2})\\(c)0.5m(2v1v2+v2^{2})\\(d)0.5m(v2^{2}-v1^{2})[/tex]
Explanation:
velocity of ball in train reference = v2
velocity of ball in earth reference = v1+v2
(a)
Kinetic energy is given by [tex]0.5mv^{2}[/tex] where m and v are the mass and velocity of object respectively.
Change in kinetic energy is given by subtracting initial kinetic energy from the final kinetic energy. In this case
Initial kinetic energy= [tex]0.5mv1^{2}[/tex]
Final kinetic energy= [tex]0.5m (v1+v2)^{2}=0.5m(v1^{2}+2v1v2+v2^{2})[/tex]
Change in kinetic energy=[tex]0.5m (v1+v2)^{2}-0.5mv1^{2}=0.5m((v1+v2)^{2})-v1^{2}=0.5m(2v1v2+v2^{2}[/tex]
(b)
Change in velocity in train reference will be
Initial kinetic energy= [tex]0.5mv1^{2}[/tex]
Final kinetic energy= [tex]0.5mv2^{2}[/tex]
Change in kinetic energy=[tex]0.5m(v2^{2}-v1^{2})[/tex]
(c)
Work done, W = change in kinetic energy=[tex]0.5m (v1+v2)^{2}-0.5mv1^{2}=0.5m((v1+v2)^{2})-v1^{2}=0.5m(2v1v2+v2^{2}[/tex]
(d)
Work done, W = change in kinetic energy=[tex]0.5m(v2^{2}-v1^{2})[/tex]
