Our 10-ft ladder from the previous problem is leaning against the wall.

Question

Our 10-ft ladder from the previous problem is leaning against the wall. If the top of the ladder slides down the wall at a rate of 2 ft/s, how fast is the bottom of the ladder moving along the ground when the bottom of the ladder is 6 ft from the wall?

Answer 1

x is the distance measure from the base of the ladder to the wall

y is the distance measur efrom the ground to the top of the ladder

x^2 + y^2 = 10^2 = 100

Implicit differentiation:

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

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

Now, when x=6, 6^2 + y^2 = 100

y^2 = 100 - 36 = 64

y = 8

Finally,

6 * dx/dt + 8 * 2 = 0

6 * dx/dt + 16 = 0

6 * dx/dt = -16

dx/dt = -16/6 = -8/3

negative because it is moving down