Answer:
[tex]-\frac{d\theta}{dt} = 0.18 rad/s[/tex]
Explanation:
As we know that the length of the ladder is given as
[tex]L = 10 ft[/tex]
now at any instant of time let the ladder is at distance "x" from the vertical wall
then the angle made with the horizontal for the ladder is given as
[tex]cos\theta = \frac{x}{L}[/tex]
now differentiate both sides with respect to time
[tex]-sin\theta (\frac{d\theta}{dt}) = \frac{1}{L} \frac{dx}{dt}[/tex]
so here we have
[tex]-\frac{d\theta}{dt} = \frac{1}{Lsin\theta}(\frac{dx}{dt})[/tex]
given that
[tex]\frac{dx}{dt} = 1.1 ft/s[/tex]
[tex]cos\theta = \frac{8}{10} [/tex]
[tex]\theta = 37 degree[/tex]
now we have
[tex]-\frac{d\theta}{dt} = \frac{1}{10 sin37}(1.1)[/tex]
[tex]-\frac{d\theta}{dt} = 0.18 rad/s[/tex]
