# calculus

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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 -

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

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