Acceleration due to gravity on the surface of a planet is `196 cm *s^(-2)`. If it is safe to jump from a height of 2m on the earth, what is the safe height for taking a jump on that planet ?

Explanation

If a man jumps from a height h and v is the velocity attained on reaching the earth.s surface , then `v=sqrt(2gh)`
Let the safe height for taking a jump on the other planet be `h^.`. In that case, velocity attained on reaching the planet.s surface is,
`v^.=sqrt(2g^.h^.)`
For the problem `v^.=v`
`therefore gh=g^.h^. or, h^.=g/(g^.)*h`
Given `g=9.8m*s^(-2)=1.96m*s^(-2)`
`and g^.=196cm*s^(-2)=1.96 m*s^(-2)`
`therefore h^.=(9.8xx2)/(1.96)=10m`
Hence , it is quite safe to take a jump from a maximum height of 10 m from the surface of the planet.