Two bodies reIeased from different heights fall freeIy and reach the ground at the same time. The first body takes a time,`t_(1) = 2`s and second body takes a time, `t_(2) = 1`s. What was the height of the first body at the time of reIease of the second body?

Explanation

Let the height from which the first body is released be `h_(1)` above the ground. When it is at a height `h_(2)` the second body is released .
So, the first body falls through a height `(h_(1) - h_(2))` in time `(t_(1)-t_(2))` before the release of the second body. According to the problem,
`h_(1) = (1)/(2) "gt"_(1)^(2)" ""and"" "h_(1)-h_(2) = (1)/(2) g(t_(1)-t_(2))^(2)`
or, `" "(1)/(2)"gt"_(1)^(2)-h_(2)=(1)/(2)g (t_(1)-t_(2))^(2)`
or, `" " h_(2) = (1)/(2)g(2t_(1)-t_(2))t_(2)`
`= (1)/(2) xx 9.8 (2xx2-1)xx1 = 14 .7 `m.