Question

A 20 meter ladder rests vertically against the side of a barn. A pig that has been hitched to the ladder starts to pull the base of the ladder away from the wall at a constant rate of 0.4 meters per second. Find the rate of change of the height of the top of the ladder after 30 seconds.

Answer 1

I hope my drawing explains well lol... h = 16

Explanation:

So basically first you need to find x (the one in the drawing), by doing so, you just have to use the formula,

`speed = (distance)/(time)`

You substitute in the speed and the time given,

`0.4 = (x)/(30) \\ x = 12`

Then, you use the Pythagorean theorem,

`h = \sqrt{ {20}^(2) - {12}^(2) } \\ h = 16`