Answer:
[tex]\dfrac{dL}{dt}=5.82 \ ft/s[/tex]
Explanation:
given,
street light height = 13 ft
man height = 6.3 ft
speed of the man = 3.5 ft/sec
[tex]\dfrac{H}{L} = \dfrac{h}{l}[/tex]
[tex]\dfrac{H}{L} = \dfrac{h}{L-x}[/tex]
[tex]\dfrac{L}{H} = \dfrac{L-x}{h}[/tex]
hL = H(L-x)
hL = HL-Hx
[tex]L = \dfrac{Hx}{H-h}[/tex]
[tex]L = \dfrac{13x}{13-6.3}[/tex]
L = 1.94 x
[tex]\dfrac{dL}{dt}=\dfrac{dL}{dx}\dfrac{dx}{dt}[/tex]
[tex]\dfrac{dL}{dt}=1.94\times 3[/tex]
[tex]\dfrac{dL}{dt}=5.82 \ ft/s[/tex]
