test Review Problem That Wasn't In Any Homework I Can Find

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SUMMARY

The discussion revolves around a mathematical problem involving a kite flying at a height of Y feet, tethered by a 100 ft string at an angle theta with the ground. Key tasks include finding the derivative dY/d(theta) and its units, calculating dY/d(theta) when Y equals 50 feet, and determining the kite's rising speed given an angular velocity of d(theta)/dT = 0.8 radians per second. Participants suggest using trigonometric relationships, specifically the sine function, to derive the necessary equations and clarify the units involved.

PREREQUISITES
  • Understanding of trigonometric functions, particularly sine and arcsine.
  • Knowledge of derivatives and differentiation techniques.
  • Familiarity with angular velocity concepts in physics.
  • Basic understanding of unit conversions, especially between feet per second and miles per hour.
NEXT STEPS
  • Study the differentiation of trigonometric functions, focusing on y = 100 sin(theta).
  • Learn about the application of the chain rule in calculus for related rates problems.
  • Explore unit conversion methods, particularly converting feet per second to miles per hour.
  • Review inverse trigonometric functions and their applications in solving for angles.
USEFUL FOR

Students preparing for calculus exams, particularly those focusing on related rates problems, as well as educators seeking to enhance their teaching strategies in trigonometry and calculus.

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Please Help...test Review Problem That Wasn't In Any Homework I Can Find!

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(theta). what are its units?
2. find dY/d(theta) when Y= 50 feet. State the units
3. if the angular velocite d(theta)/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...THIS IS A REVIEW PROBLEM FOR A TEST I HAVE ON MONDAY (TWO DAYS FROM NOW), AND IF I CAN'T FIGURE OUT HOW TO DUE THESE TYPE OF PROBLEMS, I AM IN BIG TROUBLE...
 
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This one's tough. Have you drawn it out for yourself? If you did, you know you'd have some sort of trig relationship relating the hypotenuse the opposite side and angle theta. I'm wondering, since they gave you Y but not theta, if you should use arcsine (inverse trig relation) to find theta.

arcsinx = Y/100
100arcsinx= Y
100/sqrt(1-x^2x') = YY'
.
.
.
Only problem is you end up with two unknowns using this method...oops. Y' would be the ideal thing to find on #3 but for that you need x (theta), which I am now stumped on how to find. Units for 1 and 2 would probably be feet per radian...
 
Why don't you just write y = 100 \sin \theta and differentiate?
 

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