Last update 08/05/2016.
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* For the impatient, the answer is "Yes". For those who want the details, see below.
Background: The table below reflects Earthbased physics, applied to falling
damage in D&D. It makes the use of certain assumptions which, if altered, will alter
this table and these results.
 
Mathematical Derivation
A lot of the following is available in any Physics textbook or online. It is therefore presented here with only necessary detail. Because D&D uses 10 foot intervals for falling damage (1d6 per 10' fallen), the information below will stick to English units.
Note above that damage "x" is linearly proportional to distance fallen "y". That actually justifies the D&D system where 1d6 of damage is applied to every 10 feet fallen. To exemplify this, consider the following:
Formula: For the purposes of the below chart, it is assumed that "12×m×k×g×10" pounds of force will be equivalent to "1d6" hit points of damage. (Thus were we able to 'hand wave' the lack of a definitive value of "k", as we can derive all falling damage by assigning the damage of a 10' fall to 1d6 and simply scaling everything up from there. Why Damage isn't Identical for Identical Distances Fallen: If the above assumptions are presumed to hold, then force on the falling body is identical for all falls of an identical distance. Why, then, should damage have a variable component? Why isn't a 10' fall always exactly, say 3 hit points of damage, every time? The use of dice to determine damage could be attributed to how a character lands. Although the force is the same, a character falling 10 feet and landing on their feet would likely take less damage than one who falls and lands on their head. Maximum Damage: It takes a fall of just over 480 feet to reach "terminal velocity" (176 feet/second). As such, in D&D, one can justify a maximum falling damage of 48d6 at 480'. Falls further than 480 feet will not yield more damage, as the body can not fall any faster. Massbased damage: Astute readers will note that force (and thus damage) is also directly dependent upon the mass of the falling body, lending credence to the old saying "The bigger they are, the harder they fall". For DM's wishing to add a touch of "reality" to their games, a burly human (100 kg of mass) should take twice as much damage as a gnome (50 kg of mass). Two options leap to mind:
Example: Under these two different scenarios, a 50 foot fall for an Elf would yield:

Distance Fallen (feet)  Time it took to fall that far (seconds)  Velocity at impact (ft/sec)  Impact force with 1 inch deceleration (times 12×k×g)  Damage Roll 
10 
0.788 
25.377 
m*10 
1d6 
20 
1.114 
35.888 
m*20 
2d6 
30 
1.365 
43.954 
m*30 
3d6 
40 
1.576 
50.754 
m*40 
4d6 
50 
1.762 
56.745 
m*50 
5d6 
60 
1.930 
62.161 
m*60 
6d6 
70 
2.085 
67.141 
m*70 
7d6 
80 
2.229 
71.777 
m*80 
8d6 
90 
2.364 
76.131 
m*90 
9d6 
100 
2.492 
80.249 
m*10 
10d6 
110 
2.613 
84.166 
m*11 
11d6 
120 
2.730 
87.909 
m*12 
12d6 
130 
2.841 
91.498 
m*13 
13d6 
140 
2.948 
94.952 
m*14 
14d6 
150 
3.052 
98.285 
m*15 
15d6 
160 
3.152 
101.508 
m*16 
16d6 
170 
3.249 
104.632 
m*17 
17d6 
180 
3.343 
107.666 
m*18 
18d6 
190 
3.435 
110.616 
m*19 
19d6 
200 
3.524 
113.490 
m*20 
20d6 
210 
3.611 
116.292 
m*21 
21d6 
220 
3.696 
119.029 
m*22 
22d6 
230 
3.779 
121.704 
m*23 
23d6 
240 
3.860 
124.322 
m*24 
24d6 
250 
3.940 
126.885 
m*25 
25d6 
260 
4.018 
129.398 
m*26 
26d6 
270 
4.095 
131.863 
m*27 
27d6 
280 
4.170 
134.283 
m*28 
28d6 
290 
4.244 
136.660 
m*29 
29d6 
300 
4.316 
138.996 
m*30 
30d6 
310 
4.388 
141.294 
m*31 
31d6 
320 
4.458 
143.554 
m*32 
32d6 
330 
4.527 
145.780 
m*33 
33d6 
340 
4.595 
147.972 
m*34 
34d6 
350 
4.662 
150.133 
m*35 
35d6 
360 
4.728 
152.262 
m*36 
36d6 
370 
4.793 
154.363 
m*37 
37d6 
380 
4.858 
156.435 
m*38 
38d6 
390 
4.921 
158.480 
m*39 
39d6 
400 
4.984 
160.499 
m*40 
40d6 
410 
5.0463 
162.493 
m*41 
41d6 
420 
5.107 
164.462 
m*42 
42d6 
430 
5.167 
166.409 
m*43 
43d6 
440 
5.227 
168.333 
m*44 
44d6 
450 
5.286 
170.235 
m*45 
45d6 
460 
5.345 
172.116 
m*46 
46d6 
470 
5.403 
173.977 
m*47 
47d6 
480 
5.460 
175.818 
m*48 
48d6 
Seconds Fallen  Velocity  Distance Fallen this past second  Total Distance Fallen 
0  0.0 feet/second  0 feet  0 feet 
1  32.2 feet/second  16 feet  16 feet 
2  64.3 feet/second  48 feet  64 feet 
3  96.5 feet/second  80 feet  145 feet 
4  128.6 feet/second  113 feet  257 feet 
5  160.8 feet/second  145 feet  402 feet 
6  176 feet/second*  172 feet  574 feet 
7  176 feet/second  176 feet  750 feet 
8  176 feet/second  176 feet  926 feet 
9  176 feet/second  176 feet  1102 feet 
10  176 feet/second  176 feet  1278 feet 
* The distance fallen at second 6 is calculated assuming that the faller's velocity accelerates from from 160.8 feet/second to 176 feet/second in the first 0.47 seconds and then remains constant at 176 feet/second for the last 0.53 seconds. From that point forward, air friction counters the acceleration of gravity and the faller as at "terminal velocity", unable to fall any faster.