Answer:
Ladder is moving away from the wall with the speed of 3.464 ft/s
Step-by-step explanation:
Consider the figure attached
Given that top of ladder slides down with the speed of 2ft/sec, i.e
[tex]\frac{dh}{dt}=2fts^{-1}[/tex]
Length of ladder =10 ft
bottom of the ladder is 5 ft from the wall i.e b=5
By pythagorous theorem
[tex]h^2+b^2=100---(1)\\\\h^2=100-(5)^2\\\\h^2=75\\\\h=5\sqrt{3}ft[/tex]
Differentiating equation (1) w.r.to t
[tex]2h\frac{dh}{dt}+2b\frac{db}{dt}=\\\\2(5)\frac{db}{dt}=-2(5\sqrt{3})(2)\\\\\frac{db}{dt}=-2\sqrt{3}\\\\\frac{db}{dt}=-3.464\,ft/s[/tex]
Negative sign shows that ladder is moving away from wall
