Posted by **lucky** on Sunday, June 19, 2011 at 3:59am.

A ladder , 5 meter long , standing on a horizontal floor , leans against a vertical wall . If the top of the ladder slides downwards at the rate of 10 cm/sec . Find the rate at which the angle between the floor and the ladder is decreasing when the lower end of the ladder is 2 meter from the wall .

- math -
**Reiny**, Sunday, June 19, 2011 at 8:52am
let the ladder reach h m high on the wall, let the base angle be Ø

sinØ = h/5

h = 5sinØ

dh/dt = 5cosØ dØ/dt

given: dh/dt = -10m/sec

when base = 2m, cosØ = 2/5

-10 = 5(2/5) dØ/dt

dØ/dt = -5 radians/sec

the angle is decreasing at a rate of 5 radians / sec

(by using the word "decreasing" I do not include the negative sign)

- math -
**JANARDHAN**, Monday, March 3, 2014 at 10:05am
Change first 5m to 500cm and 2m to 200cm and then solve using above procedure of reiny answer is 1/20 radians/sec

## Answer This Question

## Related Questions

- calculus - a ladder 6 feet long leans against a vertical building. the bottom of...
- Math - A 15 ft ladder leans against a wall. The bottom of the ladder is 3 ft ...
- Differential calculus - A ladder 20 ft long leans against a vertical wall, If ...
- Calculus - A 18 ft ladder leans against a wall. The bottom of the ladder is 4 ft...
- 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 ...
- Calculus - A 15 ft ladder leans against a wall. The bottom of the ladder is 4 ...
- calculus - A 25-ft ladder rests against a vertical wall. If the bottom of the ...
- Math - A ladder leans against a vertical wall and the top of the ladder is ...
- Calculus - 1a. 15 ft ladder is placed against a vertical wall. the bottom of the...

More Related Questions