Answer:
2.47 m/s
Step-by-step 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, [tex]\dfrac{dx}{dt}=3/ m/s[/tex]
Let the length of string released be s m
In right triangle using pythagoreous theorem
[tex]s^2=34^2+x^2[/tex]
For s = 60 m ,
[tex]60^2=34^2+x^2[/tex]
[tex]x=49.44[/tex] m
Differentiate the equation [tex]s^2=34^2+x^2[/tex] w.r.t t
[tex]2s\dfrac{ds}{dt}=0+2x\dfrac{dx}{dt}[/tex]
[tex]2\cdot 60\cdot \dfrac{ds}{dt}=2\cdot 49.44\cdot 3[/tex]
[tex]\dfrac{ds}{dt}=\dfrac{296.62}{120}[/tex]
[tex]\dfrac{ds}{dt}=2.47[/tex] m/s
Hence, the rate of string letting out 2.47 m/s
