SOLUTION: a 10 inch book is leaning against a bookshelf when its bottom starts to slide away. By the time the bottom is 6 inches from the side of the bookshelf, the base of the book is movin

Question 1026693: a 10 inch book is leaning against a bookshelf when its bottom starts to slide away. By the time the bottom is 6 inches from the side of the bookshelf, the base of the book is moving at a rate of 3 in/sec. How fast is the angle theta changing at that time?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
a 10 inch book is leaning against a bookshelf when its bottom starts to slide away. By the time the bottom is 6 inches from the side of the bookshelf, the base of the book is moving at a rate of 3 in/sec. How fast is the angle theta changing at that time?
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You didn't spec where angle theta is, but the change will be the same regardless.
Using the bottom of the book that is on the shelf and the shelf as the angle and b as the side on the shelf and calling the angle A:
----
cos(A) = b/10
Differentiate wrt time.
-sin(A)*dA/dt = (db/dt)/10
sin(A)*(dA/dt) = -3/10
---
Side a = 8 inches
----
dA/dt = -3/(10*0.8)
dA/dt = -0.375 rad/sec

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