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

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In summary, the kite is rising at a rate of .8 radians per second. It is climbing 50 feet in about 2 seconds.
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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.
 
  • #3
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!
 

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

1. What is a "Calc problem (dY/d? triangle)"?

A "Calc problem (dY/d? triangle)" is a type of calculus problem that involves finding the derivative of a function with respect to a specific variable or parameter, often represented as dY/d?. The triangle symbol represents the change in the variable or parameter.

2. How do you solve a "Calc problem (dY/d? triangle)"?

To solve a "Calc problem (dY/d? triangle)", you must first identify the function and the specific variable or parameter that the derivative is being taken with respect to. Then, you can use the appropriate rules of differentiation, such as the power rule or chain rule, to find the derivative. Finally, you can substitute the value of the variable or parameter for the triangle symbol to find the specific derivative value.

3. What is the purpose of solving a "Calc problem (dY/d? triangle)"?

The purpose of solving a "Calc problem (dY/d? triangle)" is to find the rate of change of a function with respect to a specific variable or parameter. This is useful in many fields, such as physics, economics, and engineering, as it allows us to understand how a system or process is changing over time.

4. Are there any common mistakes to avoid when solving a "Calc problem (dY/d? triangle)"?

Yes, there are some common mistakes to avoid when solving a "Calc problem (dY/d? triangle)". These include mixing up the order of operations, forgetting to use the chain rule when necessary, and not simplifying the final answer. It is important to carefully follow the steps and double-check your work to avoid these errors.

5. What are some real-world applications of "Calc problem (dY/d? triangle)"?

There are many real-world applications of "Calc problem (dY/d? triangle)". For example, it can be used to calculate the velocity of an object in motion, the growth rate of a population, or the rate of change of a stock price. It is also used in engineering to optimize processes and in economics to analyze supply and demand.

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