A child is flying a kite at a height of 40 ft, that is, moving horizontally at a rate of 3 ft/sec.

Question

A child is flying a kite at a height of 40 ft, that is, moving horizontally at a rate of 3 ft/sec. If the string is taut, at what rate is the string being paid out when the length of the string released is 50 ft?

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Defined variables-                                                                           

Numerical facts known about the variables and their

           derivatives with respect to t-                                                

The unknown (what you wish to find)-                                           

The equation to relate the variable that depend on t-                       

Final answer (includes the solution on differentiation)-                   

Interpretation-                                                                                  

Answer 1

Assuming that the kite is directly over the child at time t = 0,

Let x = horizontal distance travelled by the kite at time t and y = length of string at time t.

Given: dx/dt = 3. Find dy/dt when y = 50.

y² = x² + 40²

2y(dy/dt) = 2x(dx/dt)

dy/dt = x(dx/dt) / y

When y = 50, 50² = x² + 40². So, x = 30.

So, dy/dt = (30 ft)(3ft/sec) / (50 ft) = 1.8 ft/sec