Question

I have a doubt.
Why did they take final velocity = u m/s ? ​

Answer 1

Answer:

In the first case when the object is thrown up, by the third kinematical equation

(0)^2-u^2 = 2(-g)(h)

or,

h = u^2/2g

Now, in the second case clearly the ball is thrown from the space height , so again from the third kinetimatical equation

(Final velocity)^2 - (0)^2 = 2(g)*u^2/2g = u^2

Or, the final velocity will still be u, this is how we've proved it.

They should've given this explanation there rather than directly stating final velocity to be taken as u.

Still, consider this fact that most things can be rigorously found out using math however in simple dynamical system such like what has been given here, there always lie Dynamical symmetries in physical observables such as time, velocity, displacement, etc irrespective and independent of the direction in which motion of the particle occurs.

Hope this helps you ! ｡◕‿◕｡