**Tl;DR: It is mainly do to the skier's positioning on the ski and how being thrown off-balance by the avalanche affects it.**


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Concerning the first part of the first question:

> 1) If all free falling objects accelerate at the same rate (this was on a fairly steep mountain section), why did we get "trapped" into the avalanche, when our acceleration already had 35 mph +/- accelerating it?

there is probably a large *psychological component* here. You were moving across a stationary ground and suddenly that ground starts gliding, which it didn't before. So it is really the **change in its movement** that you felt.

There is also a physical component however: you state correctly that "all free falling objects accelerate at the same rat" and under this assumption it shouldn't make any difference that the ground started moving. But a **free fall approximation is not very good** for skiing, especially when you already are in motion.

> Did the thicker snow breaking and shifting somehow create more friction between my ski and the snow?

The answer is of course no, on the other this question already hints at what actually happens. Skiing is a large dependent on your **position and balancing on the ski**, and the acceleration does too (1). Our case is different from racing, but similar concepts apply. In the "dust on crust" you describe you have to **lean back slightly to float**, even with your rockers. This comes at a cost of acceleration. When the avalanche starts moving you get thrown off balance a bit, leaning back even further relative to the ground. To accelerate, you get back in front first applying the pressure to the ski as before. This takes some time of course.

> Why was it so easy for snow to sink me down, when my ski's design is for 2+ ft of snow and I was forcefully trying to "float" above the collapsing snow?

Same reason, due to the leaning back your ski doesn't float properly anymore.

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(1) which is e.g. why you we saw [Ted Ligety][1] win almost every Giant Slalom a couple of years ago: he invented a better ski position

(2) aaaah, second best after deep powder in my opinion

  [1]: https://en.wikipedia.org/wiki/Ted_Ligety