the string of a kite is being let out at a rate of 2 m/min if the angle of elevation of the kite remains constant 30 degrees, what rate is the kite climbing

Question

Calculus related problem, Math 31 alberta, Unit 3 applications of Derivatives. Its a triangle question.

Answer 1

If the angle of elevation is 30 degrees, then we have a triangle with height of 1 and hypotenuse of 2.  We want to find the base of the triangle.

 

Using an identity, the base is then √3, since cos30 = √(3)/2.

 

Next, we use the Pythagorean theorem.

 

x² + y² = L²

 

where:

x = base

y = height

L = length of string

 

Use implicit differentiation on the Pythagorean theorem.

 

2x(dx/dt) + 2y(dy/dt) = 2L(dL/dt)

 

You would want to solve for dy/dt, but you don't know what dx/dt is.  You need to find dx/dt first, then plug in the values to find dy/dt.