Asked by Stacy
a ladder is 20 feet long and its top is slidding at a constant rate of 2 feet per second. How fast is the bottom of the ladder moving along the ground when the bottom is 16 feet from the wall?
Answers
Answered by
Reiny
Let the ladder be x ft from the wall, and y ft up along the wall
x^2 + y^2 = 20^2
2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0
when x=16 , y^2 = 400-256 ---> y = 12
and dy/dt = -2 ft/sec
16(dx/dt) + 12(-2) = 0
dx/dt = -24/16 = -3/2
the ladder is moving away from the wall at 1.5 ft/s
x^2 + y^2 = 20^2
2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0
when x=16 , y^2 = 400-256 ---> y = 12
and dy/dt = -2 ft/sec
16(dx/dt) + 12(-2) = 0
dx/dt = -24/16 = -3/2
the ladder is moving away from the wall at 1.5 ft/s
Answered by
Reiny
last two lines should have been
16(dx/dt) + 12(-2) = 0
dx/dt = 24/16 = 3/2
16(dx/dt) + 12(-2) = 0
dx/dt = 24/16 = 3/2