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.