Solving for dY/d? and Finding the Rate of Change of a Kite's Height

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SUMMARY

The discussion focuses on calculating the rate of change of a kite's height (dY/dθ) using trigonometric principles and calculus. The kite is flying at a height of Y feet, with a 100 ft string making an angle θ with the ground. The participants outline the steps to derive the equation for dY/dθ, evaluate it at Y = 50 feet, and determine the kite's rising speed given an angular velocity of dθ/dT = 0.8 radians per second. The final conversion of the rising speed from feet per second to miles per hour is also discussed.

PREREQUISITES
  • Understanding of trigonometric functions and their applications.
  • Familiarity with calculus concepts, specifically differentiation and the chain rule.
  • Knowledge of unit conversion techniques, particularly between feet per second and miles per hour.
  • Ability to apply the Pythagorean theorem in practical scenarios.
NEXT STEPS
  • Learn how to derive trigonometric relationships in right triangles.
  • Study the application of the chain rule in calculus for related rates problems.
  • Practice unit conversion between different measurement systems, especially for speed.
  • Explore graphical representations of trigonometric functions to visualize changes in angles and heights.
USEFUL FOR

Students studying calculus and trigonometry, physics enthusiasts analyzing motion, and educators seeking to explain related rates in real-world applications.

skivail
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i don't understand how to figure this problem out, and i really need the help.

A kite is flying Y feet about the ground at the end of a 100 ft. string. the string makes an angle of ? (theta) with the ground.

1. find the equation for dY/d?. what are its units?

2. find dY/d? when Y= 50 feet. State the units

3. if the angular velocite d?/dT =.8 radians per second, how fast is the kite rising when Y=50 feet?

4. how fast is your answer to c in miles per hour?


I AM COMPLETELY LOST, EXCEPT FOR I AM PRETTY SURE I CAN FIGURE OUT NUMBER 4 ONCE I HAVE THE ANSWER TO NUMBER 3 SINCE THIS HAS NOTHING TO DO WITH CALCULUS. PLEASE HELP ME...
 
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oops, all of those ?'s are actually supposed to be thetas, but the computer messed it up when i posted. please help me.
 
skivail said:
i don't understand how to figure this problem out, and i really need the help.
A kite is flying Y feet about the ground at the end of a 100 ft. string. the string makes an angle of ? (theta) with the ground.
1. find the equation for dY/d?. what are its units?
2. find dY/d? when Y= 50 feet. State the units
3. if the angular velocite d?/dT =.8 radians per second, how fast is the kite rising when Y=50 feet?
4. how fast is your answer to c in miles per hour?
I AM COMPLETELY LOST, EXCEPT FOR I AM PRETTY SURE I CAN FIGURE OUT NUMBER 4 ONCE I HAVE THE ANSWER TO NUMBER 3 SINCE THIS HAS NOTHING TO DO WITH CALCULUS. PLEASE HELP ME...
OK, use pythagoras theorem and draw a diagram..
100ft will be the hypotenuse (imagine it), Y is going to be, well, y... and using trigonometry you can express x in terms of the hypotenuse and theta...
Form the equation with y = blabla with theta somewhere and then differentiate with respect to theta...
For the question about what its units are, think of the derivative-- you're finding the rate of change of Y with respect to theta... so given the unit of Y and the unit of theta, you can state the units as [unit of Y goes here] per [unit of theta goes here].
For 3, you're going to be using the chain rule; by the looks of it, you're finding dy/dT
4) Simple units conversion..

Hope I helped out some? Someone correct me if I'm wrong somewhere, please!
 

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