A ladder of length 10 metres is being drawn up a wall. The top of the ladder is

moving upwards at 1 metre per second. Find the speed with which the foot of the
ladder is approaching the wall when the foot is 6 metres from the wall.

1 answer

If x is the distance of the foot, and h is the height,

x^2 + h^2 = 10^2
so, h=8 when x=6

2x dx/dt + 2h dh/dt = 0
2(6) dx/dt + 2(8)(1) = 0
dx/dt = -4/3