Posted by **Michelle** on Sunday, July 15, 2012 at 1:50am.

a 4m ladder is leaning against a wall when its base starts to slide away. By the time the base is 2m from the wall, the base is moving at the rate of 1m/sec.

find

a) the speed at which the top of the ladder is sliding down the wall

b) the rate at which the area of the triangle formed by the ladder, wall and ground is changing.

c) the rate at which the angle theta between the ladder and the ground is changing.

Thanks!!

- maths -
**Steve**, Sunday, July 15, 2012 at 1:18pm
with x=distance of base from wall, y the height,

x^2 + y^2 = 16

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

when x=2, dx/dt=1

y = √12, so

2(2) + 2√12 dy/dt = 0

dy/dt = -4/2√12 = -1/√3

a = xy/2

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

= √12*1 - 2/√3

= 4/√3

so da/dt = 2/√3

tanθ = y/x

sec^2θ dθ/dt = (xy' - yx')/x^2

when x=2, tanθ = √12/2 = √3, so θ=π/6

sec^2θ = 4/3, so

4/3 dθ/dt = (2(-1/√3)-(√12)(1))/4

dθ/dt = -√3 / 2

as always, double-check my algebra

## Answer this Question

## Related Questions

Calculus - A 40-foot ladder is leaning against a house when its base starts to ...

calculus - A 13 ft ladder is leaning against a house when its base begins to ...

Calculus Please Help!! - "A 13-foot ladder is leaning against a building when ...

CALCULUS HELP!! - I haven't done this type of problem in a while, so if someone ...

Calculus - A 13 foot ladder is leaning against the house when it's base starts ...

Calculus - A ladder is leaning against the wall of a house.The base of the ...

Calculus - a 5m ladder rests against a vertical wall. The top of the ladder ...

Calc. - A ladder 25ft long is leaning against the wall of a house. The ladder is...

Calculus - not sure if my work is correct? - A 15ft ladder leans against a ...

calculus - A 13 foot ladder leaning against a wall makes an angle of degree ...