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a $25$ foot ladder is resting against a wall so that the bottom of the ladder is $7$ feet from the wall. the bottom of the ladder starts slipping away from the wall at a rate of $1$ foot per second. how many feet per second is the top of the ladder sliding down the wall when it is $15$ feet above the ground?



Answer :

The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. When the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.

Given that,

The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. A feet per second of the ladder's bottom begins to slide away from the wall.

We have to find when the ladder is 15 feet above the ground, how many feet per second is the top of the ladder falling down the wall.

Let us take x = height where the ladder hits the building

7 squared + x squared=25 squared

49+x squared=625

x squared=576

x=24 feet

Now,

If it slips 15 feet that 24-15=9 feet

Let x = distance from wall:

x² + 9² = 25²

x² + 81= 625

x² = 544

x = 23.3 feet

Therefore, when the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.

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