Answer:
The length of the beam increasing is 9.64 ft/s.
Explanation:
Given that,
Height = 210 ft
Distance =290 ft
According to figure,
We need to calculate the angle
[tex]\cos\theta=\dfrac{210}{x}[/tex]....(I)
Put the value of x in the equation
[tex]\cos\theta=\dfrac{210}{290}[/tex]
[tex]\cos\theta=\dfrac{21}{29}=0.72[/tex]
Now, [tex]\sin\theta=\dfrac{20}{29}[/tex]
On differentiate of equation (I)
[tex]-\sin\theta\dfrac{d\theta}{dt}=-\dfrac{-210}{x^2}\dfrac{dx}{dt}[/tex]
[tex]\sin\theta=\dfrac{210}{x^2}\dfrac{dx}{dt}[/tex]
Put the value in the equation
[tex]\sin\dfrac{20}{29}\times2.0=\dfrac{210}{(290)^2}\dfrac{dx}{dt}[/tex]
[tex]\dfrac{dx}{dt}=\sin\dfrac{20}{29}\times2.0\times\dfrac{290^2}{210}[/tex]
[tex]\dfrac{dx}{dt}=9.64\ ft/s[/tex]
Hence, The length of the beam increasing is 9.64 ft/s.
