Hello everyone,

This is my first post here - I look forward to looking around to see what goes on here.

Anyway, I'm a mechanical engineering senior, taking a vector kinematics class. And I've been stumped all evening. I suspect I'll feel dumb when somebody points out why this is occuring (hoping it's just due to sleep deprivation lol), but I can't for the life of me figure out how the solution I am looking at is doing away with a pair of terms.

I'd like to think I have a pretty decent grasp on this material, but the 4th picture I posted (whole problem is spread over 4 photos) is throwing me for a loop. I'm good with it until they say "Simplifying" and drop two of the r_2 velocity terms. I've looked at a number of answers in the solutions I found online and they all seem to drop a term at the end for no apparent reason. My textbook is still on backorder and google hasn't turned up much that's relevant. I have literally spent the last 6 hours puzzling over this, so I will be tremendously grateful to anyone who can shed some light on it. Why do the r_2'Cos(theta_2) and r_2'sin(theta_2) terms just vanish without warning during the "simplifying" phase?

https://www.facebook.com/photo.php?f...9&l=4026c64019
https://www.facebook.com/photo.php?f...8&l=140208c71d
https://www.facebook.com/photo.php?f...9&l=fa3ca6dbd2
https://www.facebook.com/photo.php?f...1&l=c6c539a698
Thanks.

-Patrick