How Do I Find the Horizontal Distance of a Bug on a Moving Ladder?

[nicnic20]

Homework Statement

So I've seen this posted here already but I'm still completely clueless on how to start the problem.

Problem: A 30-foot ladder rests vertically against a wall. A bug starts at the bottom of the ladder and climbs up at a rate of 3.5 feet per minute. At the same time, the foot of the ladder is being pulled along the ground at a rate of 1.5 feet per minute until the top of the ladder reaches the ground. Let x be the distance of the bug from the wall at time t.



Question: Find the function x(t). This function gives the horizontal distance of the bug to the wall as a function of time, t.

Homework Equations

The Attempt at a Solution

So I'm not sure where to begin when finding x(t). I started with the Pythagorean theorem because of the obvious triangle and came up with x^2 + y^2= 30. Now I'm stuck.

 

[Dick]

It's not that hard. Figure out how far the bug has gone along the ladder at time t. Then figure out what the cosine of the angle the ladder is sitting at time t. Use some trig. Or similar triangles, your choice. BTW I think we should call this "the famous bug problem". Let's give the bug his due.

 

[nicnic20]

I'll call it the famous bug on the infamous ladder problem.
I'm sure I am making it 100x more complicated than it actually is.


So I figured out the bug is at 3.5t/30 am I correct?

 

[Dick]

I'll call it the famous bug on the infamous ladder problem.
I'm sure I am making it 100x more complicated than it actually is.


So I figured out the bug is at 3.5t/30 am I correct?

At time t the bug will be 3.5*t feet along the length of the ladder. The bottom of the ladder will be 1.5*t feet from the wall. If you draw a picture, you should see some right triangles to solve.