Instantaneous Speed Application Problem

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Homework Statement



My teacher put us into groups and we each selected a wall of the rectangular room. He attached some sort of machine to the wall that spins in a circle with a laser on it, creating a laser point revolving around the walls. Our task is to create a function for the instantaneous speed of the laser point at any point x on our wall.

2. The attempt at a solution
1. We found the dimensions of the room. The red dot indicates where the laser is at. We have the left wall.
calc.png

2. We found the RPM by counting how many times the laser hit one spot on the wall over a interval of 1 minute.
RPM = 36
3. Converted to radians per second 6pi/5

Now we don't know what to do from here.
 
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How about defining some variables to represent the relevant quantities in your problem? For instance, you referred to "x". What is x?
 
X would be any distance on our wall from 0 to 26.75.
 
Measured from where? You need to precisely define the quantities here. We can't read your mind. Are there any other variables?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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