## anonymous 5 years ago A television camera is positioned 10000 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 its speed is 800 ft/s when it has risen 24000 ft. (Round the answers to three decimal places.) (a) How fast is the distance from the television camera to the rocket changing at that moment?

1. anonymous

its easy....first let the camera and rocket in line position..,,,when the rocket has risen find the distance between rocket and camera by using phytagoras theorema.. $\sqrt{10000^2+ 24000^2}$ = 676000000 ft then v =x \t t can be found,,then the velocity of rocket from camera view can be found by the same equation..

2. amistre64

dr/dt = dr/dy * dy/dt or implicitly derive the pythagorean theorum and fill in what you know :)

3. amistre64

Ill implicit it... x^2 + y^2 = r^2 10000^2 = r^2 - y^2 dx/dt 2(10000) = dr/dt 2r - dy/dt 2y divide it all by "2" to simplify: (dx/dt) 10000 = (dr/dt)r - (dy/dt)y dx/dt = 0 ; dy/dt = 800 ; y=24000; and r= sqrt(10000^2 - 24000^2) 0 = (dr/dt)sqrt(10000^2 - 24000^2) - (800)(24000) solve for dr/dt...

4. amistre64

dr/dt = 800(24000) - sqrt(10000^2 - 24000^2) happy number crunching :)

5. anonymous

Thank you

6. amistre64

ack!! sign error lol

7. amistre64

sqrt(10000^2 + 24000) sneaky little bugger it is :)

8. amistre64

your smart; youll be able to read thru the typos lol

9. amistre64

Just for eruditional purposes..... dr/dt = 800(24000) - sqrt(10000^2 + 24000^2)

10. amistre64

...... murmur...... still got errors in it..... if you can work the algebra, be by guest :) 0 = (dr/dt)sqrt(10000^2 + 24000^2) - (800)(24000) (800)(24000) = (dr/dt)sqrt(10000^2 + 24000^2) (800)(24000) ------------------------ = (dr/dt) sqrt(10000^2 + 24000^2) Maybe? with a little luck? better double check it :)

11. anonymous

sure, thanks yahoo, thank you so much, answer is correct

12. amistre64

LOL .... that makes us BOTH happy :)