A ladder of length 10 m rests with its lower end on a horizontal floor and with a rate of 2m/sec when the lower end is at 8m away from the wall, find: 1) the rate of sliding of the upper end. 2) the rate of change of the angle between the ladder and the floor

Answer 1

A ladder of length 10 m rests with its lower end on a horizontal floor and with a rate of 2m/sec when the lower end is at 8m away from the wall, find:
1) the rate of sliding of the upper end.
2) the rate of change of the angle between the ladder and the floor

Answer 2

x^2+y^2=10^2
y=6 when x=8

tanθ = y/x, so
y = x tanθ
tanθ=3/4 when x=8

x dx/dt + y dy/dt = 0
dy/dt = tanθ dx/dt + x sec^2θ dθ/dt

Now just plug in your numbers.