The top of a ladder slides down a vertical wall at a rate of 0.375 m/s.

Question

At the moment when the bottom of the ladder is 6 m from the wall, it slides away from the wall at a rate of 0.5 m/s. How long is the ladder?

Answer 1

Let x = distance from bottom of the ladder to the wall

Let y = distance from top of the ladder to the floor

Let z = the length of the ladder

When x = 6, dx/dt = 0.5 m/s

dy/dt = -0.375 m/s (sliding down, so negative)

dz/dt = 0 (The ladder length is constant)

z²=x²+y²

2z dz/dt = 2x dx/dt +2y dy/dt

0= 2(6)(0.5) + 2y(-0.375)

y = 3/0.375 = 8 m

z²=36+64

z=10 m

Answer 2

l² = x² + y²; 0 = 2xdx/dt + 2ydy/dt; dx/dt = 0.5 m/s; dy/dt = - 0.375 m/s, x = 6m. So, 12·0.5 - 0.75y = 0; y =

6/0.75 = 8 m; l = √(6² + 8²) = 10 m