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December 22, 2014

December 22, 2014

Posted by **Robin** on Wednesday, July 3, 2013 at 10:38am.

How fast is the distance from the camera to the rocket changing in ft/s at that moment?

If the televison camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing in radians/s at that moment

- Please help with Calc problem?? -
**Reiny**, Wednesday, July 3, 2013 at 10:58amIt would help if we knew the distance of the camera to the launch pad, which would give us a constant.

The way you have it involves 3 variables:

the angle, the height, and the distance between rocket and camera.

Are you sure there wasn't more information?

- Please help with Calc problem?? -
**Robin**, Wednesday, July 3, 2013 at 11:00amSorry, I meant a television camera is positioned 2500 ft from the base of a rocket launching pad. The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. Also the mechanism for focusing the camera has to take into account the increasing distance from the camera to the rising rocket. Let's assume the rocket rises vertically and that its speed is 800 ft/s when it has risen 4000 ft.

How fast is the distance from the camera to the rocket changing in ft/s at that moment?

If the televison camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing in radians/s at that moment?

- Please help with Calc problem?? -
**Reiny**, Wednesday, July 3, 2013 at 11:25amok, that's better

make a sketch of the situation, labeling the angle as Ø and the height as h, and the hypotenuse c.

preliminary:

when h = 4000

c^2 = 2500^2 + 4000^2

c = 4716.99

tanØ = 4000/2500 = 1.6

Ø = 57.995°

at that moment: we have a similar triangle with base 5, height 8 and hypotenuse √89

cosØ = 5/√89 ----> needed later

sinØ = 8/√89 ----> needed later

secØ = √89/5 ----> needed later

tanØ = h/2500

2500tanØ = h

2500 sec^2Ø dØ/dt = dh/dt

2500(89/25) dØ/dt = 800

dØ/dt = 25(800)/(2500(89)) = .08988764

in general:

sinØ = h/c

csinØ = h

c cosØ dØ/dt + sinØ dc/dt = dh/dt

for our given:

4716.999(5/√89) (.08988764) + (8/√89) dc/dt = 800

I will leave it up to you to do the "button-pushing" to find dc/dt

also, please check my arithmetic

- Please help with Calc problem?? -
**Steve**, Wednesday, July 3, 2013 at 12:18pmI haven't checked my answer against Reiny's, but I also took a stab at it in

http://www.jiskha.com/display.cgi?id=1372720314

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