How believable is a story like "The Cold Equations"? What examples from the story make you think this?
On a scientific level, the universe described in "The Cold Equations" might be unrealistic or a bit contrived, but the human emotions described in the story are believable. For example, the scenario presented at the beginning of the story is a bit contrived, as galactic expansion has made space travel very difficult and expensive. Therefore, hyperspace cruisers can not deviate from their schedules, or they will risk causing confusion that could destroy the relationship between earth and her colonies. For this reason, Barton, the pilot of the Emergency Dispatch Ship, must destroy Marilyn, the young stowaway aboard his ship.
This scenario might be a bit contrived, and it is difficult to determine the scientific veracity of it, as we have not progressed to this level of space travel. However, the human emotions of the characters are very believable. The pilot dreads having to jettison Marilyn from his ship, which will be fatal to her. He is particularly aware of Marilyn's vulnerability and innocence. She only wanted to get aboard the ship to visit her brother, and she tearfully writes her loved ones and manages a quick call with her brother before perishing. The emotions of these characters are very believable, though the setting is not entirely realistic.
Tom Godwin's short story "The Cold Equations" is realistic and believable. The use of space travel in the story is for colonization, exploration and trade. The consequences of the extra weight of the girl on the ship's deceleration is explained in terms that are understandable and logically in sync with physics. The time frame of how long the girl can stay on the ship is explained in detail. The decision to jettison the girl is the only one that could possibly be made; the survival of the colony outweighs the life of the girl. It is also consistent that a young girl would make an impulsive decision to stow away on the ship. One of the few things that is not realistic is the length of time verbal messages take to travel to and from the girl's brother in the colony.
Consider the differences between this and other, unrealistic space travel stories. There is usually a plot device that (as far as we know) is impossible, such as time travel, or faster-than-light travel. Various alien species usually inhabit these universes; there are no known alien species. We are constantly on the lookout for some, though!