Posted by **Jeff** on Monday, October 26, 2009 at 3:22am.

A flag pole is 40 feet high and stands on level ground. a flag is attached to a 120 foot rope passing through a pulley at the top of the flagpole. The other end of the rope is tied to a car at ground level. If car was driving directly away from flagpole at 3ft/sec, how fast is flag rising when top of flag is 20 ft off ground?

- calculus -
**Reiny**, Monday, October 26, 2009 at 8:15am
At a time of t seconds,

let the height of the flag be h feet, then the distance to the top of the pole is 40-h feet and length of rope from the top of the pole to the car is 80+h feet.

let the car be x feet from the base of the pole.

given: dx/dt = 3 ft/s

fing: dh/dt , when h = 20

I see Pythagoras here,

x^2 + 40^2 = (80+h)^2

2xdx/dt = 2(80+h)dh/dt

dh/dt = xdx/dt/(80+h)

when h = 20

x^2 + 1600 = 10000

x = 8400

x = √8400

finally

dh/dt = √8400(3)/100

= 2.47 feet/second

## Answer this Question

## Related Questions

- another math - At a distance of 34 feet from the base of a flag pole, the angle ...
- Math - At a distance of 56 feet from the base of a flag pole, the angle of ...
- geometry - A wire is attached to the top of a flag pole. The wire meets the ...
- Thinking Mathematically - solve A Flag Pole Has A Height Of 16 Yards. It Will Be...
- physcis - a flag pole is 1ooft from an observer who sights the top of the flag ...
- math - An observer stands 25 feet from the base of a 50 foot flagpole and ...
- Geometry - Michael is standing in the middle of a playground at night looking at...
- math - A 5-foot tall women is standing near a flag pole which casts a shadow of ...
- Algebra - Scott set up a volleyball net in his backyard. one of the poles, which...
- business math - a 4 foot post that is 8 feet from a flag pole is casting a ...