Answer:
[tex]\frac{dy}{dt}=1.2\frac{mi}{min}[/tex]
Explanation:
We know that the tangent function relates the angle of the right triangle that forms the hot air balloon rising:
[tex]tan\theta=\frac{y}{x}\\y=xtan\theta(1)[/tex]
Differentiating (1) with respect to time, we get:
[tex]\frac{dy}{dt}=tan\theta\frac{dx}{dt}+xsec^{2}\theta\frac{d\theta}{dt}\\[/tex]
[tex]\frac{dx}{dt}=0[/tex] since x is a constant value. Replacing:
[tex]\frac{dy}{dt}=3mi(sec^{2}\frac{\pi}{3})0.1\frac{rad}{min}\\\frac{dy}{dt}=1.2\frac{mi}{min}[/tex]
