Mr. Cook was painting Arvada West High School, standing on top of a 25�]foot ladder. Why? We will never

know. However, he was horrified to find the ladder being pulled away by the same notorious student that
threw a snowball at Mrs. Evans. The base of the ladder was moving from the school at a constant rate of 2
feet per second.
8) At what rate was the top of the ladder carrying him down toward the ground when the base of the ladder
was 17 feet away from AWest?

draw the triangle.

b^2+h^2=25^2
2b db/dt+ 2h dh/dt=0
solve for h (sqrt (25^2-b^2)
you know db/dt, b, h, solve for dh/dt

poopy pants

To find the rate at which the top of the ladder was carrying Mr. Cook down toward the ground, we can use related rates.

Let's identify the knowns and unknowns in this problem:
- Knowns:
- The height of the ladder = 25 feet
- The rate at which the base of the ladder is moving away from the school = 2 feet per second
- The distance between the base of the ladder and AWest (the point of reference) = 17 feet

- Unknown:
- The rate at which the top of the ladder is being carried down toward the ground

Now, we can set up a relationship between the known and unknown variables. We can consider a right triangle formed by the ladder, the ground, and a vertical line from the top of the ladder to the ground.

We can use the Pythagorean theorem to relate the height of the ladder to the distance between the base of the ladder and AWest:

(Height of ladder)^2 = (Distance between base of ladder and AWest)^2 + (Distance from the top of the ladder to the ground)^2

Taking the derivative of both sides with respect to time, we get:

2 * (Height of ladder) * (Rate at which the top of the ladder is being carried down) = 2 * (Distance between base of ladder and AWest) * (Rate at which the base of the ladder is moving away) + 0

Simplifying the equation, we have:

(Height of ladder) * (Rate at which the top of the ladder is being carried down) = (Distance between base of ladder and AWest) * (Rate at which the base of the ladder is moving away)

Now we can plug in the known values:

(25 feet) * (Rate at which the top of the ladder is being carried down) = (17 feet) * (2 feet per second)

Solving for the rate at which the top of the ladder is being carried down, we have:

Rate at which the top of the ladder is being carried down = (17 feet) * (2 feet per second) / (25 feet)

Calculating this, we get:

Rate at which the top of the ladder is being carried down = 1.36 feet per second

Therefore, when the base of the ladder was 17 feet away from AWest, the top of the ladder was carrying Mr. Cook down toward the ground at a rate of 1.36 feet per second.