Answer:9.75 m/s
Explanation:
Given
Length of ladder [tex](L)=5 m[/tex]
Foot the ladder is moving away with speed of [tex]\frac{\mathrm{d} x}{\mathrm{d} t}=13 m/s[/tex]
From diagram
[tex]x^2+y^2=L^2[/tex]------1
at [tex]x=3 [/tex]
[tex]y^2=25-9=16[/tex]
[tex]y=4 m[/tex]
Now differentiating equation 1 w.r.t time
[tex]2x\frac{\mathrm{d} x}{\mathrm{d} t}+2y\frac{\mathrm{d} y}{\mathrm{d} t}=0[/tex]
[tex]x\frac{\mathrm{d} x}{\mathrm{d} t}=-y\frac{\mathrm{d} y}{\mathrm{d} t}[/tex]
[tex]3\times 13=-4\times \frac{\mathrm{d} y}{\mathrm{d} t}[/tex]
[tex]\frac{\mathrm{d} y}{\mathrm{d} t}=-\frac{3\times 13}{4}=-9.75 m/s[/tex]
negative indicates distance is decreasing with time
