Answer:
Given, length of the ladder = 5 cm = 500 cm Let \[\theta \] be the angle between floor and ladder, then \[\sin \theta =\frac{y}{500}\] On differentiating w.r.t. ?t?, we get \[\cos \theta \frac{d\theta }{dt}=\frac{1}{500}\cdot \frac{dy}{dt}\] It is given that\[\frac{dy}{dt}=10\,\,cm/\sec \] \[\therefore \] \[\cos \theta =\frac{x}{500},\]when \[x=200\] \[\Rightarrow \] \[\cos \theta =\frac{200}{500}=\frac{2}{5}\] Substituting the respective values, we get \[\frac{2}{5}\frac{d\theta }{dt}=\frac{1}{500}\times 10\] \[\Rightarrow \] \[\frac{d\theta }{dt}=\frac{1}{50}\times \frac{5}{20}=\frac{1}{20}rad/s\]
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