/sci/ - Science & Math

/sci/, I have a question. It's about something I stumbled on while doing homework, but I'm not asking for help with the actual problem. I've solved that already, and I'm confident in my result. But one of my approaches for checking my answer doesn't work the way I thought it would, and I'm losing sleep trying to figure out why.

To paraphrase the problem: an airplane takes off and climbs at a constant 12 degrees, at 430 mph. What's it's rate of elevation gain when it's half a mile high?

I solved it using two different approaches, both taking the derivative of the hypotenuse of a right triangle modeling the plane's flight, both yielded some decimal value just over 113 ft/second (IIRC). Checked it half a dozen times; this is the right answer.

Early on, I figured a quick and dirty way to verify my answer would be this:

If the airplane were flying straight up (90 degrees), obviously it's rate of elevation gain would be the same as its airspeed, and the speed over ground would be zero, right? And if it were flying parallel to the ground, the opposite is true. So I should be able to treat it like a ratio: 12/90= X, multiply airspeed by X, and badabing, there's the rate of climb at 12 degrees.

Except it doesn't work. Ends up coming out low (something like 85 feet per second, IIRC). I've gone over it again and again, verified that I'm converting units correctly, etc, and I am. Cannot for the life of me figure out the flaw in my thinking, and it's gnawing at me something fierce.

Can anyone identify the nature of my idiocy?

What was the hardest course in your major?
Is it the course everyone says is the hardest?
>dude (random course) is so hard it will either make or break your major

>>7583798
I literally only got maybe an hour last night because I procrastinated studying.
Today is going to kill me.