How fast do those things shoot out from the jewelweed pods?

An experimental verification, while walking through the woods
If you've ever walked through the woods in eastern Massachusetts on a crisp fall morning, you know the unique pleasure of touching the seed pods of the pale jewelweed plant, Impatiens pallida, and watching them explode everywhere. It's pretty amazing.[1]
Yes, we actually have Impatiens pallida around here, not just its more common relative Impatiens capensis!
[2]
Those of you among the audience who are hardcore Harry Potter fans should've immediately recognized Jewelweed as a crucial ingredient in Fergus Fungal Budge.
One obvious question to ask is, given this whole fancy biological mechanism, how fast do the seeds actually leave the pod? For instance, Morus alba, the white mulberry tree, shoots out pollen at the speed of sound,[3]
Taylor, P.E., Card, G., House, J. et al. High-speed pollen release in the white mulberry tree, Morus alba L. Sex Plant Reprod 19, 19–24 (2006). https://doi.org/10.1007/s00497-005-0018-9
so plants seem pretty well-adapted to the problem of launching projectiles!
Anyways, here's the video I got on my walk:
The pod shoots out four seeds in different directions. For the sake of measurement (for now), let's focus on the seed that gets shot out parallel to the groud—this one:
The seed that we're analyzing is circled.
That way, we can just measure the speed based on the dimensions of the field of view, and we don't need to account for upward motion. Let's trace out the path that the seed takes:
The seed path
So, sixteen frames. All right, so, how far does that seed travel before it hits my wallet? Well, we know that the dimensions of a Frontier Series five-Canadian dollar note are 152.4mm by 69.85mm...actually, I still have the note I used in the video, so let's just take a photo of a ruler next to it:
A ruler next to a Canadian $5.
Sorry, Wilfried! Your beautiful face isn't in any of these photos.
And then align it with the $5 note from the video:
The seed path with a ruler superimposed
And rotate it to measure the distance:
The measured length
So the seed we looked at travels roughly 41.5 millimeters in 15 frames, which at 480 fps comes out to 31.25 milliseconds. As a result, the speed of the seed is $$\frac{41.5 \text{ mm}}{31.25 \text{ ms}} \approx 1.328 \text{ m}/\text{s} = 2.971 \text{mph}.$$
Wow, what a lame speed. I can outrun one of those without even trying. Let's check with what Hayashi, Feilich, and Ellerby[4]
Marika Hayashi, Kara L. Feilich, David J. Ellerby, The mechanics of explosive seed dispersal in orange jewelweed (Impatiens capensis), Journal of Experimental Botany, Volume 60, Issue 7, May 2009, Pages 2045–2053, https://doi.org/10.1093/jxb/erp070
had to say when they masured it in a laboratory setting:
Table 1 from Hayashi et al.
Source: Table 1 from [4]
1.24±0.4 m/s, they say. We got 1.33 m/s; not too far.[5]
One caveat is their paper was done on Impatiens capensis, and my video was of the less common Impatiens pallida, but it's probably close enough.
Here's one interesting thing I'd like to point out. Watch the video again:
If you look carefully, you'll see that one of the seeds is flying hella upward, but its horizontal velocity component is pretty much exactly as fast as that of the seed whose speed we measured! By Pythagoras or whatever, this means that that seed got expelled much faster—assuming, say, a 60 degree angle, it would've travelled $$41.55 \sec\left(60^{\circ}\right) \text{ mm} \approx 83 \text{ mm},$$ and that's, like, 2.66 meters per second, which is almost 6mph! I'm not sure I can outrun that.
If you'd like to cite this article, you can use this: 
@misc{gritsevskiy2020jewelweed,
  author = {Gritsevskiy, Andrew},
  title = {How fast do those things shoot out from the jewelweed pods?},
  year = {2020},
  howpublished = {Blog post},
  url = {https://andrew.fi/stories/jewelweed/}
}