Question

A 18 ft ladder leans against a wall. The bottom of the ladder is 4 ft from the wall at time t = 0 and slides away from the wall at a rate of 2ft/sec. Find the velocity of the top of the ladder at time t = 2. The velocity of ladder at time t =

Answer 1

The velocity of the top of the ladder at time t = 2 is 2 ft/sec.

Step-by-step explanation:

To find the velocity of the top of the ladder at time t = 2, we can use the concept of similar triangles.

At time t = 0, the bottom of the ladder is 4 ft from the wall. At time t = 2, the bottom of the ladder has slid away from the wall at a rate of 2 ft/sec for 2 seconds, so the distance between the bottom of the ladder and the wall is 4 + (2 * 2) = 8 ft.

Since the ladder is always leaning against the wall, the height of the ladder remains the same. Therefore, the ratio of the distances between the bottom and the top of the ladder and the wall remain the same. We can set up the following proportion:

(height of ladder) / (distance between bottom of ladder and wall) = (height of ladder) / (distance between top of ladder and wall)

Let's call the distance between the top of the ladder and the wall x. Solving for x:

(18 ft) / 8 ft = (18 ft) / x

Cross multiplying and solving for x:

8 * x = 18 * 18

x = (18 * 18) / 8

x = 40.5 ft

Therefore, the distance between the top of the ladder and the wall at time t = 2 is 40.5 ft.

Since the ladder is sliding away from the wall at a rate of 2 ft/sec, the velocity of the top of the ladder at time t = 2 is also 2 ft/sec.

Answer 2

The velocity of the top of the ladder at time t = 2 is 2 ft/sec.

Step-by-step explanation:

To find the velocity of the top of the ladder at time t = 2, we can use the concept of similar triangles. We know that the bottom of the ladder is 4 ft from the wall at time t = 0 and slides away from the wall at a rate of 2 ft/sec. Therefore, at time t = 2, the bottom of the ladder will be 4 + (2 x 2) = 8 ft from the wall.

Since the ladder leans against the wall, the distance of the top of the ladder from the wall will also increase at a rate of 2 ft/sec. Therefore, at time t = 2, the top of the ladder will be 8 + (2 x 2) = 12 ft from the wall.

So, the velocity of the top of the ladder at time t = 2 is 2 ft/sec.