# YAMT: Simple Calculus Related Rates

#### speg

##### Diamond Member
Ugh, a question I could do with my eyes closed 7 months ago is taking me three hours, and 7 attempts to do now. I eventually got it after being stupid with Arctan, but I want to do it another way, so yeah....

A television camera at ground level is filming the lift off of a rocket that is rising vertically with a postition s = 25t^2 m, where t is in seconds. Find the rate of change of the angle after 10 seconds.
They give you the diagram, noting that the distance from the camera to the rocket at launch is 1000 m

So it's a simple triangle with the base of 1000 m constant and the height of 25t^2.

So this is what I did ( let x represent the angle, since I can't find no delta symbol on here ):

tanx = s/1000

1000tan(x) = s
1000tan(x) = 25t^2
derive w/ respect to t
1000 [sec(x)]^2 dx/dt = 50t
dx/dt = 50t * 1/1000 * [tan(x)]^2
dx/dt = 1/2 * [ 2500 / 1000 ] ^2
dx/dt = 3.125

But that's wrong, the answer is 2/29. Which I eventually got using arctan, but I want to do it this way. I can do it this way right? Bah!! Final in 4 hours :S

#### Red

##### Diamond Member
Riiiiiiight.

YACT = Yet another car thread

#### DurocShark

##### Lifer
Shouldn't your subject be "YAMathT"?

#### speg

##### Diamond Member
Math / Calculus / Car, meh

#### speg

##### Diamond Member
*cough*bump*cough*

I finished the rest of the practice exam, hopefully this will go smoothly. T-Minus 2.5 hours! Ahh!

#### speg

##### Diamond Member
Bump!

Exam went pretty smoothly. Missed one question, but other than that, A-OK.

OMG. I am such a moron. After almost 3 or 4 hours with this damn thing I finally realized that secx = 1/cos, not 1/tan. Damnit brain why don't you work anymore?!!! AHHHHHHHH!!!!!!!!!!!