Question #282118

A kite , at a height of 60 ft. is moving

horizontally at a rate of 5ft/sec. away from

the boy who flies it. How fast is the string

being released when 100 ft. are out.


1
Expert's answer
2021-12-23T06:24:16-0500

Let l be the length of the cord and x - horizontal distance.

l2=x2+602.l^2=x^2+60^2 .

2ldldt=2xdxdt2l\frac{dl}{dt}=2x\frac{dx}{dt} .

dldt=xldxdt.\frac{dl}{dt}=\frac{x}{l}\frac{dx}{dt}.

When l=100 ft, x=1002602=80  ft.x=\sqrt{100^2-60^2}=80\;ft.

So, dldt=801005=4  ft/sec.\frac{dl}{dt}=\frac{80}{100}*5=4\;ft/sec.


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