**Let us assume,**

The velocity with which the elevatar ascends be u', the height attained by elevatar at time,T_{1} be h .

**Thus,**

u' = \(\frac{h}{T_1}\)

**Equation of motion,**

h = -u'T_{2} + \(\frac{1}{2}gT_2^2\)

∵ u' = \(\frac{h}{T_1}\)

h + \(\frac{h}{T_1}\)T_{2} = \(\frac{1}{2}gT_2^2\)

h(1 + \(\frac{T_2}{T_1}\)) = \(\frac{1}{2}gT_2^2\)

h = \(\frac{1}{2}\)\(\frac{gT_2^2}{(1+\frac{T_2}{T_1})}\)