Answer:3.75 ft/s
Explanation:
Given
Length of ladder(L)=40 feet
base of ladder moves at a rate of 5 ft/sec
Bottom of ladder from wall(x)=24 feet
let horizontal distance be x and vertical distance be y
[tex]y=\sqrt{40^2-24^2}=32[/tex]
therefore
[tex]x^2+y^2=L^2[/tex] from Pythagoras
differentiate
[tex]2x\times \frac{\mathrm{d} x}{\mathrm{d} t}+2y\frac{\mathrm{d} y}{\mathrm{d} t}=0[/tex]
[tex]x\times \frac{\mathrm{d} x}{\mathrm{d} t}=-y\times \frac{\mathrm{d} y}{\mathrm{d} t}[/tex]
[tex]24\times 5=-32\times \frac{\mathrm{d} y}{\mathrm{d} t}[/tex]
[tex]\frac{\mathrm{d} y}{\mathrm{d} t}=\frac{-3}{4}\times 5=-3.75 ft/s[/tex]
negative sign indicates height is decreasing
