Homework Help: math

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 Ų
sinŲ = h/5
h = 5sinŲ
dh/dt = 5cosŲ dŲ/dt

given: dh/dt = -10m/sec
when base = 2m, cosŲ = 2/5

-10 = 5(2/5) dŲ/dt
dŲ/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)

Answer this Question

Related Questions

math - a ladder 6 meters long leans against a wall. It rests on the ground 1 ...
math - A uniform ladder of length 2a and mass m lies on a vertical plane with ...
Math - A painter leans a ladder against a vertical wall. The top of the ladder ...
math - A painter leans a ladder against a vertical wall. The top of the ladder ...
math - A painter leans a ladder against a vertical wall. The top of the ladder ...
physics - A 150-kg ladder leans against a smooth wall, making an angle of 30 ...
physics - Bill the firefighter stands on an 8 meter ladder of weight 355 Newtons...
Physics - A Ladder of length L and mass m leans against wall at angle theta from...
math - A ladder leans against a brick wall, The top of the ladder touches the ...
mathematic - A ladder 10 meter long is leaning against a wall. If the top of ...

For Further Reading

First Name:
School Subject:
Answer: