Question

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.

Answer 1

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

$l^2=x^2+60^2 .$

$2l\frac{dl}{dt}=2x\frac{dx}{dt}$ .

$\frac{dl}{dt}=\frac{x}{l}\frac{dx}{dt}.$

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

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