At the end of the first Banjo-Kazooie game, Gruntilda is sent falling off the top of her layer and crashing into the ground below:

Starts at 8:11.

She not only survived the fall, she also survived a very heavy rock falling on top of her.

So it's up to me to find out the kinetic energy of both events. This is one of the few feats in Banjo-Kazooie that I know about that's separated from game mechanics so I'd say it's pretty important.

The first order of business is figuring out Gruntilda's mass.

Note the picture below:

Spoiler:

Banjo is 70 pixels. The tree he's adjacent to is 315 pixels in height.

Now, Chaos revealed to me over the course of this conversation, that Cable would typically use a height of ten meters for a tree, so that's what I'll use here. If any of you know the species of tree that this might roughly correspond to, let me know.

315/70 = 4.5
10/4.5 = 2.2

Meaning Banjo has a height of 2.2 meters. Not too surprising for a bear I suppose.

Moving on.

Spoiler:

When comparing Banjo to Dingpot, Banjo in this shot is 88 pixels. Dingpot on the other hand is 128 pixels from foot to rim.

128/88 = 1.45
2.2 x 1.45 = 3.19

So Dingpot's height is 3.19 meters. We also see that Dingpot's rim is about 14 pixels high.

128/14 = 9.14
3.19/9.14 = 0.3 meters or 30 centimeters.

Again moving on.

Spoiler:

In this shot, Gruntilda is 196 pixels above Dingpot's rim. The rim in the meantime is 39 pixels.

196/39 = 5.025

Remembering now that the rim was 30 centimeters tall:

30 x 5.025 = 150.75

Meaning Gruntilda is 150.75 centimeters taller than the bottom of the rim.

319 - 30 = 289

The bottom of the rim is therefore 289 centimeters or 2.89 meters tall.

289 + 150 = 439.

So Gruntilda's height is 4.39 meters, confirming my suspicion that she's pretty damn big. Now it's time to scale this bitch's considerable girth.

Spoiler:

In this shot her total height is 291 pixels. Her diameter is 195 pixels, not counting her clothes, of course.

291/195 = 1.4
4.39/1.4 = 3.1 meaning this bitch is fucking fat.

Now comes something trickier. I need to get her width so I can get her volume (an ellipsoid) thankfully, I've got another shot.

Spoiler:

Her height here is 44 pixels. Her width is 32.

44/32 = 1.3

4.39/1.3 = 3.3

Christ this bitch is a fatty.

Now I have everything I need to get her volume, which is the radii of her width, length, and height (so half of those above values).

Using this calculator, I got a total volume of 22.44 m^3.

Now I need to get her mass in kilograms, which is density times volume. For her density, I'll just assume average human density which is around 1010 kg/m^3 (check my Kinniku calc).

1010 x 22.44 = 22,664.4 kilograms.

Oh boy.

As I showed above, Gruntilda's fall starts at 8:11. There are two screen black outs between 8:17-8:19 and 8:28-8:29 or about four seconds. She lands at 8: 33.

Minus those four seconds (and this was deemed alright in my Galvatron calc so it shouldn't be a problem here), the fall was eighteen seconds.

Free fall as we know is 9.8 m/s^2 Gruntilda fell for eighteen seconds.

9.8 x 18 = 176.4. So that was her speed at final impact.

Now comes the really fun part, calculating the kinetic energy of the fall.

ke=1/2mv^2.

22,664.4/2 x 176.4^2 = 352,623,614.11200005 joules. Still less than a ton, but that's still much much more than an entire Tour de France race.

However, that still isn't the end of the story, because notice that Gruntilda tanked a gigantic boulder falling on top of her after her first fall.

Spoiler:

Now, Banjo's height here is 66 pixels. The height of the rock is 277 pixels.

277/66 = 4.1
2.2 x 4.1 = 9.02

The rock's diameter is 424 pixels from widest point to widest point.

424/66 = 6.4
2.2 x 6.4 = 14.08

Moving on for the final time.

Spoiler:

Banjo's height in this final scaling is 69 pixels. The width of the rock is more or less 340 pixels.

340/69 = 4.9
2.2 x 4.9 = 10.78

Turning again back to the ellipsoid volume calculator, the volume of this ellipsoid comes out as being 715.055 m^3. Now as to its density, the typical thing to go with is granite. The density of solid granite is 2,691 kg/m^3.

Remembering that mass is density times volume, the rock's mass comes out as being:

2,691 x 715.055 = 1,924,213.005 kilograms.

Assuming that the rock fell from the same height as Gruntilda but a bit after her fall began, it would have been falling for again, eighteen seconds.

ke=1/2mv^2

1,924,213.005 x 176.4^2 = 29,937,829,554.032402 joules.

Converting that to tons, the number comes out as being 7.1553129909.

And Gruntilda tanked that without a scratch.

Final Recap:

Gruntilda's fall: 352,623,614.11200005 joules.
Rock's fall: 7.1553129909 tons.

So Gruntilda's durability is in the large building range.