. 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
D)–12.25 ft/sec
E) –0.75 ft/sec

Question

.  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
D)–12.25 ft/sec
E)  –0.75 ft/sec

anonymous · Answer

first write the position of the top as a function of the position of the bottom

anonymous · Answer

How do I do that? please explain in detail

anonymous · Answer

although if you don't have to show your work, you can just guess the sensible answer

anonymous · Answer

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?

anonymous · Answer

Hint.|dw:1326760267836:dw|

anonymous · Answer

pathagoren Theorem?

anonymous · Answer

Yes, sounds true to me

anonymous · Answer

So then I take the derivative of the Theorem?

anonymous · Answer

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.

anonymous · Answer

so should my derivative read $$dy/dx=(-2x+2c)/(2y)$$ ?