AP CALCULUS

A girl is flying a kite at a height of 320 ft. If the wind blows the kite horizontally at a rate of 15 feet per second away from the girl, at what rate is the girl releasing the string when the length of the string is 400 ft?

[kite] <---15 ft/sec
. .
. .
. .
. .
. .
. .
320 ft .
. .
. .
. .
._____________.[girl]

So I listed my given data:
a=320 ft
b=240 ft
c=400 ft

And I know I have to find dc/dt when c=400 ft - using the Pythagorean theorem. I differentiated it but now I realize that I don't have da/dt and db/dt...what do I do?

  1. 👍
  2. 👎
  3. 👁
  1. I can see from your data that you labeled your triangle with a, b, and c
    a being the vertical (fixed at 320) , b the horizontal and c the hypotenuse (the string)

    so c^2 = b^2 + 320^2
    you also found correctly that if c= 400, b = 240
    differentiate ...
    2c dc/dt = 2b db/dt + 0
    dc/dt = b db/dt/c
    = 240(15)/400 = 9

    check my arithmetic

    1. 👍
    2. 👎
  2. I was going to mention, that since a is a constant, da/dt = 0 as seen above.

    1. 👍
    2. 👎
  3. Ohh thank you-that is what I had overlooked: the fact that the derivative of a constant is = to 0 and that is why I did not need da/dt. Thank You I understand where I went wrong now.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Pre-ALgreba

    A kite flying in the air has a 12 - ft line attached to it. Its line is pulled taut and casts a 10 - ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.

  2. math

    Sam is flying a kite. The length of the kite string is 80 meters, and it makes an angle of 75° with the ground. The height of the kite from the ground is... A.20.27 B.61 C.77.27

  3. math

    A kite which is flying at a height of 215 m above the ground level descends at the rate of 5m per minute . Find its height from the ground after 30 minutes

  4. Maths

    Two observers P and Q 15m apart observe a kite in the same vertical plane and from the same side of the kite.The angle of elevation of the kite from P and Q are 35 degree and 45 degree respectively.Find the height of the kite to

  1. Algebra

    A pilot flew a 400-mile flight in 2.5 hours flying into the wind. Flying the same rate and with the same wind speed, the return trip took only 2 hours, with a tailwind. What was the speed of the wind?

  2. Math

    A kite flying in the air has an 11-ft line attached to it its line is pulled taut and casts a 9-ft shadow find the height of the kite If neccessary, round your answer to the nearest tenth

  3. Calculus

    A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 60 ft is given by y = 150 − 1/40(x − 50)^2. Find the distance traveled by the kite. (Round your answer to one decimal

  4. math

    Richard is flying a kite. The kite string makes an angle of 57 degress with the ground. If Richard is standing 100 feet from the point on the ground direcly below the kite, find the length of the kite string.. Please help!!!

  1. math

    when a child flying a kite has let out 50 m of string the string makes an angle of 55 degrees with the ground. how high is the kite

  2. Pre-Cal

    A kite string is 400 ft. long. If the kite makes an angle of 42 with the ground, what is the height of the kite?

  3. Math

    A kite flying at a height of 55m is attached to a string which makes an angle of 55 degrees with the horizontal. What is the length of the string

  4. math

    a boy is flying a kite from a string of length 150m. if the string is taut and makes an angle of 67 degrees with the horizontal,what is the height of the kite

You can view more similar questions or ask a new question.