A 9.94-m ladder with a mass of 21.6 kg lies flat on the ground. A painter grabs the top end of the ladder and pulls straight upward with a force of 226 N. At the instant the top of the ladder leaves the ground, the ladder experiences an angular acceleration of 1.71 rad/s2 about an axis passing through the bottom end of the ladder. The ladder's center of gravity lies halfway between the top and bottom ends.

and the qeustion is...

To solve this problem, we need to find the length of the ladder and the distance between the center of gravity and the bottom end. Here's how we can do it:

1. Let's start by finding the length of the ladder. We know that the ladder lies flat on the ground, so the distance between the top and bottom ends is the length of the ladder. In this case, the length of the ladder is given as 9.94 m.

2. Next, we need to find the distance between the center of gravity and the bottom end of the ladder. Since the center of gravity lies halfway between the top and bottom ends, we can divide the length of the ladder by 2. Therefore, the distance from the center of gravity to the bottom end is 9.94 m / 2 = 4.97 m.

Now that we have the necessary values, we can proceed to solving the problem. Let's find the torque acting on the ladder and the moment of inertia of the ladder:

3. The torque acting on the ladder is calculated using the formula: torque = force * distance. In this case, the force applied by the painter is 226 N, and the distance from the bottom end (where the axis of rotation passes through) to the center of gravity is 4.97 m. Therefore, the torque is given by: torque = 226 N * 4.97 m = 1125.22 N*m.

4. Next, let's find the moment of inertia of the ladder. The formula for the moment of inertia of a rod rotating about one end is: moment of inertia = (1/3) * mass * length^2. Since the ladder rotates about the bottom end, we use this formula. The mass of the ladder is given as 21.6 kg, and the length of the ladder is 9.94 m. Therefore, the moment of inertia is: moment of inertia = (1/3) * 21.6 kg * (9.94 m)^2 = 731.08 kg*m^2.

Now that we have the torque and the moment of inertia, we can calculate the angular acceleration of the ladder:

5. The torque is related to the angular acceleration by the formula: torque = moment of inertia * angular acceleration. Rearranging the formula, we find that angular acceleration = torque / moment of inertia. Plugging in the values, we get: angular acceleration = 1125.22 N*m / 731.08 kg*m^2 = 1.54 rad/s^2.

Therefore, the angular acceleration of the ladder is 1.54 rad/s^2.