Math CentralQuandaries & Queries


Question from Veronica, a student:

A man flies a kite at a height of 120 meters. The wind carries the kite horizontally away from him at a rate of 8 meters/second. How fast is the distance between the man and the kite changing when the kite is 130 meters away from him?

Hi Veronica,

In my diagram the man is at $M,$ the kite is at $K$ and$ $O is 120 m directly overhead of $M.$


The horizontal distance from O to K is $h(t) \mbox{ meters }$ and the length of the cord holding the kite is $c(t),$ both at time $t$ seconds. You know that $h^\prime(t) = 8$ meters/second.

Use Pythagoras Theorem to find an expression for $c(t).$ Differentiate both sides of this expression with respect to $t$ and evaluate at the time when $h(t) = 130 \mbox{ meters. }$ Use your expression for $c(t)$ to find its value at this time.


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