Question
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
Answers
khaled
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
1) the rate of sliding of the upper end.
2) the rate of change of the angle between the ladder and the floor
Steve
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.
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.