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 15ft ladder rests against a vertical wall. If the top of the ...
 AP calc bc  A 25ft 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 ft...
 calculus  A 25ft 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