Question

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when its base is 7 feet from the wall?

Answer 1

Answer: 6.86 ft per second

Step-by-step explanation:

Both the top and the bottom of the ladder will be moving at the same time.

Given that the base of the ladder is pulled away from the wall at a rate of 2 feet per second when its base is 7 feet from the wall. Then the time will be

Speed = distance/time

2 = 7/t

t = 7/2 = 3.5 seconds

Using pythagorean theorem to get the length L of the wall

L^2 = 25^2 - 7^2

L = 24

The ladder will move down the length at the same time.

Rate = 24/3.5

Rate = 6.86 ft/s

Answer 2

Answer: The top of the ladder moving down the wall at a rate of 0.583 ft/sec

Step-by-step explanation: Please see the attachments below