A person can jump to a height of 3 m at the equator of the Earth. Considering the same initial velocity for jumping, to what height can he jump at the poles? The radius of the Earth at the poles and the equator is 6357 km 6378 km, respectively.
Given, `(6357)/(6378) = 0.9967`

Explanation

The maximum height attained by a body is given by, `H = (u^(2))/(2g)`
In the case of a person taking a high jump, his initial velocity is ame but 'g' is different. We can write down
`(H_(1))/(H_(2))=(g_(2))/(g_(1)) rArr (H_(1))/(H_(2)) = ((R_(1))/(R_(2)))^(2)`
where `H_(1) and H_(2)` are heights attained by the person at pole and equator, respectively, and `R_(1), R_(2)` are radii at pole and equator respectively. Substituting the values,
`H_(1) = 3 xx ((R_(1))/(R_(2)))^(2) = 3 xx((6357)/(6378))^(2) = 2.98 m`