A15-ft ladder rests against a vertical wall. if the top of the ladder slides down the wall at a rate of 0.33 ft/sec, how fast, in ft/sec, is the bottom of the ladder sliding away from the wall, at the instant when the bottom of the ladder is 9 ft from the wall? answer with 2 decimal places. type your answer in the space below. if your answer is a number less than 1, place a leading "0" before the decimal point (ex: 0.35).

Let the corner of the wall and floor is our origin

Now the end of the ladder is on the floor is at distance x and top end on the wall is at distance y from this corner.

So we will use Pythagoras Theorem to find the length of the ladder.

now if we differentiate whole equation with time

now the speed of the end of the ladder at the end of the floor will be given as

here is the speed of end of the ladder on the wall.

so here we also know that

now we will plug in all values in the equation

so the end of the ladder on the floor will move with speed v = 0.44 ft/s