. A 25 ft ladder is leaning against a vertical wall. The bottom of the ladder is pulled horizontally away from the wall at 3 ft/sec. Determine how fast the top of the ladder is sliding when the bottom of the ladder is 15 ft from the wall.
A) –4 ft/sec
B) –2.25 ft/sec
C) –13.375 ft/sec
E) –0.75 ft/sec
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first write the position of the top as a function of the position of the bottom
How do I do that? please explain in detail
although if you don't have to show your work, you can just guess the sensible answer
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Put the bottom of the ladder at (x,0) and the top of the ladder at (0,y). How would you write the constraint requirement that the ladder is length 25?
Yes, sounds true to me
So then I take the derivative of the Theorem?
Yes, if you're in the Implicit Differentiation section. If you want to do it a longer easier way, just write y as a function of x, then replace x by (3t) because x(t) = 3t and differentiate your y(t) with respect to t at time t=5 because x=15.
so should my derivative read \[dy/dx=(-2x+2c)/(2y)\] ?