Sheldon enrolls in an engineering class taught by Prof. Boucher, an Army Corps of Engineers veteran who does things such as locking the classroom door at the start of class to deter late students, and assigning numbers to the students instead of learning their names. Initially, Sheldon loves this behavior, but when he does the first assignment (building a bridge) and turns it in early, Prof. Boucher rips it up and throws it in the trash, and refuses to tell Sheldon what he did wrong. Sheldon complains to President Hagemeyer, but she can't do anything because Prof. Boucher is tenured. Sheldon then decides to step up his game and figure out what he did wrong by himself.
After many failed attempts at the assignment, Sheldon asks George Sr. to talk to Prof. Boucher, since they were both in the Army. George agrees, but Prof. Boucher convinces him that Sheldon needs to figure it out on his own. While working on it outside before class, Sheldon finally realizes what he did wrong: he forgot to take into account wind force, which is relevant in engineering but not physics (which Sheldon is used to). Sheldon then completes his assignment... only to lose track of time and arrive late to class. That is why adult Sheldon hates engineering so much.
Meanwhile, Dale's ex-wife June injured her knee after slipping on a glob of hair gel at her salon, and Connie and Dale decide to help take care of her while she recovers. At one point, Dale helps June take a shower, which Connie doesn't approve of. June defends herself and Dale by saying that there aren't any other people who she would feel comfortable having them assist her in taking a shower. Connie and June then talk to each other about how much they have each "polished" Dale over the years that they have been with him.
At the end, President Hagemeyer calls Prof. Boucher into her office again, but it turns out that she only wanted to hear about Sheldon's reaction when he realized that he was late to class.
