OK, I'm gonna start with #2 and then go to #1.

2) You drop a heavy object from a height of 10 feet, and when it hits the ground it has a velocity of y. What would be the velocity if you drop it from 20 feet? From 40 feet?

20 feet = √2y.

40 feet = 2y.

This seems fairly unintuitive to me. The way I think of it is when the object falls the first ten feet, it will spend a certain amount of time falling in the 0-10 feet range. But as it continues falling, it will spend less time in the 10-20 foot range (eta: giving it less time to accelerate), as it's already moving fairly fast. So in order for the falling object to double its speed, it needs to fall another 30 feet instead of the original 10 feet, for a total of 40 feet.

This might make more sense if I could create a graph. Maybe I will if I have the time.

I thought that they were less likely to survive if the window was sufficiently low that they didn't have time to get in a safe landing position.

A cat can wrench itself around pretty fast -- when my cat rolls off the bed or sofa or whatever (he's not too bright) he still can generally land feet-down.

Really? I thought that they were less likely to survive if the window was sufficiently low that they didn't have time to get in a safe landing position.

Okay, revise my statement for ita-level specificity: a cat thrown from a 10-story window is just as likely to survive as a cat thrown from a 5-story window, or whatever the minimum cat-flip-over-land-on-feet height is. (My experience with clumsy cats is that the minimum may be as little as 6 feet.)

Upside: better commute. Downside: no office

I'm not willing to get up at the buttcrack of dawn for an office. I have skewed priorities.

OMG, I am starving like WOAH. (Do people still say that? Hmmm.) I think I need to go get lunch, which is ridiculous, I know.

1) You are driving a car, and you accelerate from 0 to 25 mph. Say the amount of energy required is x. Now you continue to accelerate from 25 mph to 50 mph. What is the total amount of energy you used to accelerate from 0 to 50 mph?

OK, my intuition would be 2x. Because if you're accelerating at the same rate, it would take x energy to go 0-25 and then x more to go from 25-50. But that's wrong. It's actually 4x. That seems really unintuitive, which prompted me to do much thinking to reconcile that.

The weird thing (to me) is that an object moving twice as fast as another object (of the same weight) has four times the energy, not two. The way I finally got an intuitive understanding of that is to think of dropping an object from ten feet, and it having a velocity of y when it hits the ground. Now to get the velocity to be double that, you would have to drop the object from four times as high, not two times. It seems intuitive that carrying an object up to 40 feet would take four times the energy than carrying it up to 10 feet. Then when you drop it from forty feet it would only have twice the velocity as from 10 feet. But it would still have four times the energy.

Damn, this is difficult to explain - have I just confused everyone so far?

(to be cont.)

Ack! Jesse, you just reminded me that I didn't bring a lunch today. (I ate all my deli turkey [intended for a sandwich] last night.)

Hmm. Am tempted to go next door to Chipotle and get a burrito bigger than my head....

Cats haven't reached terminal velocity in falls that short though, they just have more time to flip themselves over into landing position. I think they'd hit terminal velocity about the same time as similarly dense human beings... somewhere around 60 stories, isn't it?

I'm not willing to get up at the buttcrack of dawn for an office. I have skewed priorities.

Yeah, additional sleep, even just fifteen minutes or so, will make me happy. Or maybe more, depending on how I shift my hours.

Of course, once I've spent some time without an office, I'll probably be whining about how I'd trade a little sleep for my office back.

Why am I thinking about this? I believe that to really get an understanding of physics (or math, or science in general) it's much better to get an intuitive grasp of what's going on rather than just memorizing formulas. But it's weird to me that the physics of motion and energy seems so damn unintuitive, which made me obsessed with actually getting that intuitive understanding.