Why the answer in book does not match the clue given

[Buffu]

Homework Statement

An elevator ascends from the ground with uniform speed. At time $T_1$ a boy drops a marble through the floor. The marble falls with uniform acceleration $9.8$ m/s^2 and hits the ground $T_2$ seconds later. Fiind the height of the elevator at time $T_1$. Clue : if $T_1 = T_2 = 4$ then $h = 39.2m$.

Homework Equations

The Attempt at a Solution

I let the uniform speed be $u$,

The displacement is $-h$ in time $T_2$.

$-h = uT_2 - \dfrac{1}{2}g T_2^2$

Also
And $u = \dfrac{h}{T_1}$

So, $-h = \dfrac{hT_2}{T_1} - \dfrac{1}{2}gT_2^2$

Combining them I get

$h = \dfrac{ g T_2^2 T_1}{2(T_2 + T_1) }$

Is the correct ?

But the given answer is $h = \dfrac{T_1}{T_2}\dfrac12g(T_1 - T_2)^2$

Also there answer does not match the given clue ? is the given answer wrong ?

 

[TSny]

Looks like your answer is correct.

Their answer appears to correspond to having $T_2$ be the total time since $T = 0$ rather than the time since $T_1$. But, that's not the correct meaning of $T_2$ according to the statement of the question.

 

[Buffu]

Looks like your answer is correct.

Their answer appears to correspond to having $T_2$ be the total time since $T = 0$ rather than the time since $T_1$. But, that's not the correct meaning of $T_2$ according to the statement of the question.

I guess the solution manual was not created by the original authors.