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A sliding ladder A 13-ft ladder is leaning against a house
Chapter 3, Problem 23E(choose chapter or problem)
Problem 23E
A sliding ladder A 13-ft ladder is leaning against a house when its base starts to slide away (see accompanying figure). By the time the base is 12 ft from the house, the base is moving at the rate of 5 ft sec.
a. How fast is the top of the ladder sliding down the wall then?
b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
c. At what rate is the angle between the ladder and the ground changing then?
Questions & Answers
QUESTION:
Problem 23E
A sliding ladder A 13-ft ladder is leaning against a house when its base starts to slide away (see accompanying figure). By the time the base is 12 ft from the house, the base is moving at the rate of 5 ft sec.
a. How fast is the top of the ladder sliding down the wall then?
b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
c. At what rate is the angle between the ladder and the ground changing then?
ANSWER:
Solution
Step 1 of 3
In this problem we have to use the given diagram to find the following.
Given that ,
and
and
(a) First find how fast is the top of the ladder sliding down the wall.
In the diagram we see that
.’. Ladder sliding down the wall at .