A KITE 100 FT ABOVE THE GROUND MOVES HORIZONTALLY AT A SPEED OF 8 FT/S - Related Rates Triangle

A kite 100 ft. above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out?

This related rates kite problem is a good example of a related rates triangle problem. Even if you don't have this specific problem required for homework, this related rates kite angle problem is a good demonstration of techniques that can be used in other related rates problems dealing with changing angles and triangles. That's because it can be solved using the same 4 step process as all other related rates calculus word problems:

0:00 A kite 100 ft. above the ground moves horizontally at a speed of 8 ft/s
0:57 Draw a sketch
4:17 Come up with your equation
7:54 Implicit Differentiation
10:04 Solve For the Desired Rate of Change

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[JakesMathLessons]

0:00 A kite 100 ft. above the ground moves horizontally at a speed of 8 ft/s
0:57 Draw a sketch
4:17 Come up with your equation
7:54 Implicit Differentiation
10:04 Solve For the Desired Rate of Change

[JoeSwick]

my friend you just got another subscriber ... searched and searched and you broke it down . major thanks

[johnnolen]

Very thorough (and absolutely correct) but you didn't need to slog through any of it.

dθ/dt = dθ/dx · dx/dt.

In this case, θ = arccot(x/100).
d[cot(θ)]/dθ = - csc^2(θ) = - (200/100)^2 = - 4.

By the inverse function theorem then dθ/dx = 1/100 × 1/( - csc^2(θ)) = 1/100 × ( - 1/4) = - 1/400.

Therefore, dθ/dt = - 1/400 × 8/1 = - 1/50 radians per second. ◼

[watcher]

helping me learn for my exam next week, thanks!

[abdulsaburharuna]

Please can you show how you got -1/50 I got 2

[kellenbutler]

If you could make these videos shorter it would be great. Most watching are studying for an exam and already know most of, if not all, of the steps and just need a review.