As we know that as per Newton's II law we have
[tex]F = \frac{dP}{dt}[/tex]
here we will have
[tex]dP [/tex] = change in momentum
[tex]dt[/tex] = time interval in which momentum is changed
now in order to have least injury during jumping we need to have least force on the jumper
so in order to have least force we can say that the momentum must have to change in maximum time so that amount of force must be least
So we need to increase the time in which momentum of the system is changed