Issue with book's solution for a block projected up an....

[CVRIV]

Hello everyone:) I'm having an issue with an example problem in the book I'm using.

I attached a pic of the problem and the book's solution.

The issue I'm having is that I have no idea how the book got the velocity it did via the solution it presented. When I worked out the problem myself, before looking at the book's solution, I arrived at the very same solution, but I was receiving non-real results, because the magnitude within the square root is negative. That's when I peaked at the book only to find that the book did what I did, except the book has 2.5m/s. I have no idea how it came to that.

I didn't want to just write that down without having some kind of explanation. Can you help me out? Is the book wrong? Am I wrong? What am I missing here?

 

[haruspex]

same solution, but I was receiving non-real results, because the magnitude within the square root is negative

I do not see how you got that from the expression in the solution. Did you forget that (-x)² is +x²?
Please post your working.

 

[CVRIV]

I figured out what I did wrong. I was using a mass of 5kg instead of 0.5kg.

The crazy thing is that I acquired the correct value for part A using the wrong amount of mass! What happened was I didn't square the x variable so with those two mistakes, I got the right answer. Ha ha.

Thanks for your help.