TITLE: Calculate time for which a mass is in free fall
QUESTION [0 upvotes]: So I am trying to remember my childhood doing some Physics problems, but seems that I forgot almost everything. But it's not a big thing... that's why I'm training!
My problem is pretty basic although I remember just a little... let me ennounce it:

A $5\ \rm kg$ block of ice falls away from the edge of the roof of a block of
  flats, at a height of $26\ \rm m$ above the ground. Ignoring air drag, find
  out:
a) how long it takes for the ice block to hit the ground. b) what is
  the speed at which the ice block hits the ground. c) how much energy
  it transfers to the surroundings when it comes to a stop and break
  into pieces. ($g = 9.8\ \rm m/s^2$)

For a), I tried: $t = \frac{d}{r}$, and gives me $2.653\ \rm s$.
For b), I tried: $9.8 \times 2.653$, and this results in $25.9994\ \rm m/s$
For c) I tried nothing since I don't remember what should I do.
Can someone take a look at this problem and tell me if I am doing it right, or just messing all the things?

REPLY [1 votes]: Unfortunately, you are messing up quite a bit. d/g gives 2.653 s${}^2$.
You should re-read about free fall in any basic physics book. There, you'll see that when you have constant acceleration (in this case, its $g$), the height as a function of time is
$$y(t) = y_0+v_0\,t+1/2\,g\,t^2$$
where $y_0$ and $v_0$ are your starting height and speed, and $y(t)$ is the height at instant $t$. You can solve for the final time knowing that the initial speed is zero, and the distance the block falls is $H=y(t_f)-y_0$. The final expression is also in any book.
The final speed can also be calculated from the equation for speed:
$$v(t) = v_0 + g\,t$$
For the energy question, I could give you the formula, but I rather suggest that you first understand clearly the basic concepts of kinematics and dynamics before going to the next level of abstraction that is mechanical energy.

REPLY [0 votes]: Welcome to physics.stackexhange Peter! The results that you calculated are not correct. What you need are the basic equations of motion $$\begin{align}
& v   & = &u+at              \\
& s   & = &ut + \tfrac12 at^2 \\
\end{align}$$
With the initial velocity $u$, the acceleration due to gravity $a=g$. For c) you need the kinetic energy of a moving body or the potential energy of your block before the fall.
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