Assuming that the car in problem 12 is initially at rest and holds n men, each of mass m, prove that if the men run with relative velocity `v_(rel)` and jump in succession they can impart to the car a greater velocity than if they all run and jump simultaneously.
[Hint : When the men run together, the effect is the same as for one man of mass nm.
`:.Delta v=(nm)/(M+nm)v_(rel.)`
When they run and jump in succession,
`Deltav = sum_(i=1)^(i=n) =(mv_(rel))/(M+im)=mv_(rel)((1)/(M+m)+(1)/(M+2m)+(1)/(M+3m)+...+(1)/(M+nm))`]

Answer

N//a