This is just an exercise in implict differentiation.
At the moment in question, we have a 24-32-40 right triangle, with height=24.
Let θ be the angle between the ladder and the ground.
Let the base be x, and the height be y.
x^2 + y^2 = 40^2
2x dx/dt + 2y dy/dt = 0
2(32)(4) + 2(24) dy/dt = 0
dy/dt = -16/3
so, the top is sliding down at 16/3 ft/s
a = 1/2 xy
da/dt = 1/2 (y dx/dt + x dy/dt)
da/dt = 1/2 (24(4) + 32(-16/3))
= -112/3 ft^2/s
y/x = tanθ, so
y = x tanθ
dy/dt = tanθ dx/dt + x sec^2θ dθ/dt
-112/3 = 3/4 (4) + 32 (5/4)^2 dθ/dt
dθ/dt = -121/150 rad/s
Answer this Question
AICE math - A 30 foot ladder is leaning against a house(see figure). if the base...
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 ...
math - a 15 foot ladder is leaning against a house with the base of the ladder 4...
Geometry - A 12 foot ladder is leaning against a house. If the top of the ladder...
geometry - A painter leans a 15 ft ladder against a house. The base of the ...
calculus - A 13 ft ladder is leaning against a house when its base begins to ...
math - A ladder is leaning against the side of a house and forms an angle of 66o...
math - a 15 foot ladder is leaning against a house. The base of the ladder is 4 ...
trigometry - 1. A 16-foot ladder on ground level is leaning against a house. If...