Posted by **Connie** on Sunday, December 9, 2012 at 6:21pm.

A ladder leans against a vertical wall and the top of the ladder is sliding down the wall at a

constant rate of 1/2 ft/sec. At the moment when the top of the ladder is 16 feet above the

ground, the bottom of the ladder is sliding away from the wall (horizontally) at the rate of

2/3 ft/sec. At what rate will the bottom of the ladder be sliding away from the wall when the

top of the ladder is 12 feet above the ground?

- Math -
**Steve**, Sunday, December 9, 2012 at 7:52pm
if the ladder base is x feet from the wall and reaches y feet high and the ladder length is a,

x^2+y^2 = a^2

2x dx/dt + 2y dy/dt = 0

we are told that dy/dt = -1/2

so, when y=16,

2x (2/3) + 2(16)(-1/2) = 0

x=12

so, x^2+y^2 = 12^2+16^2 = 20^2

when y=12, x=16, and we have

2(16) dx/dt + 2(12)(-1/2) = 0

dx/dt = 3/8

## Answer This Question

## Related Questions

- Calculus - 1a. 15 ft ladder is placed against a vertical wall. the bottom of the...
- calculus - a ladder 6 feet long leans against a vertical building. the bottom of...
- math - the top of a ladder 6 m long is resting against a vertical wall on a ...
- Calculus! - A 16 ft. ladder leans against a wall, with the top being 12 ft. from...
- calculus - A 15-ft ladder rests against a vertical wall. If the top of the ...
- AP calc bc - A 25-ft ladder rests against a vertical wall. If the bottom of the ...
- Calculas - A 13ft ladder is placed against a verticle wall. Suppose the bottom ...
- calculus - A 25-ft ladder rests against a vertical wall. If the bottom of the ...
- Calculus - A 15 ft ladder is placed against a vertical wall. the bottom of the ...
- caculus - A 10-ft ladder rests against a vertical wall. If the bottom of the ...

More Related Questions