Question

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

Answer 1

A ladder 25 feet long is leaning against a house.  The base of the ladder is pulled away at a rate of 2 ft/sec.  

a.)  How fast is the top of the ladder moving down the wall when the base of the ladder is 12 feet from the wall?

Answer:

dy/dt = -1.094ft/sec

Explanation:

Given that:

dz/dt = 0,

dx/dt = 2,

dy/dt = ?

Hence, we have the following

Using Pythagoras theorem

We have 25ft as the hypotenuse, y as the opposite or height of wall, and x as the base of the triangle

X² + y² = z²,

12² + y² = 25²,

y² = 25² - 12²

y = √481

Therefore, we have the following:

2x dx/dt + 2y dy/dt,

= 2z dz/dt,

= 12 (2) √481 dy/dt,

= √481 dy/dt = -24,

= dy/dt = -1.094ft/sec

Therefore, final answer is -1.094ft/sec