Question

A girl flies a kite at a height 34 m above her hand. If the kite flies horizontally away from the girl at the rate of 3 m/s, at what rate is the string being let out when the length of the string released is 60 m? Assume that the string remains taut.

Answer 1

2.47 m/s

Explanation:

A girl flies a kite at a height 34 m above her hand.

It is vertical height of kite, 34 m

The horizontal rate of kite,
`(dx)/(dt)=3/ m/s`

Let the length of string released be s m

In right triangle using pythagoreous theorem

`s^2=34^2+x^2`

For s = 60 m ,

`60^2=34^2+x^2`

`x=49.44` m

Differentiate the equation
`s^2=34^2+x^2` w.r.t t

`2s(ds)/(dt)=0+2x(dx)/(dt)`

`2\cdot 60\cdot (ds)/(dt)=2\cdot 49.44\cdot 3`

`(ds)/(dt)=(296.62)/(120)`

`(ds)/(dt)=2.47` m/s

Hence, the rate of string letting out 2.47 m/s