The first one is just future in the past. The present form would be: The plane is arriving at eight. This means it is expected to arrive at this time. You could also use present simple, assuming it is a scheduled event: The plane arrives at eight. When speaking about the past, we can only use the continuous form to talk about the future (in the past), as the simple form would tell me about a completed action. The plane was arriving at eight. - expected to arrive at this time. The plane arrived at eight. - it arrived at this time The second sentence is a a kind of interrupted action. The time reference is the unspoken 'now'. The tram was arriving at the foot of the hill (at this specific time). - the tram had started to arrive but hadn't finished arriving All actions have a duration, however long or short, and simple or continuous is not really used to show this. Using continuous allows you to talk about other things happening during another action. It also has other uses, such as referring to the future or emphasising process over result.

You're absolutely right to question the use of "was arriving at" in these sentences, as "arrive" is typically a punctual verb—something that happens at a specific moment rather than over time. Generally, we’d use "arrived at" to mark a single event. However, the past continuous form ("was arriving") can still be used with "arrive" when emphasizing the process of approaching a specific point. This might be done to create suspense, set the scene, or show that the arrival is part of an ongoing narrative at that moment. In these sentences: "The plane was arriving at eight." This would usually sound more natural as "The plane arrived at eight." But if you're describing a situation in which the arrival was anticipated or happening as part of another action, the continuous form can work, like: "The plane was arriving at eight, and we were all waiting eagerly." "A tram was just arriving at the hill foot." Here, "was arriving" suggests the tram was in the final stage of arrival, just coming to the base of the hill. It gives a sense of the tram’s approach rather than the exact moment it stopped, which can be effective for descriptive or narrative writing. In both cases, "was arriving" is possible, but "arrived" would be more straightforward for punctual descriptions, unless there's a need to emphasize the process or context.

I will talk about #1. Similar comments can be made for #2. Present participles do not have precise meanings. Without context, it is impossible to say exactly what #1 means. Anything you read about present participles is likely to be only partially correct. For example, it is often said that they refer to "continuing action". That can be true, but it is not always true. This is why people can give conflicting interpretations for #1, and all of them can be correct. The only thing that can be said with certainty is that in #1, "arriving" is an adjective whose meaning is somehow connected to the verb "to arrive". Only context can allow you to determine a more precise meaning. Here are some possible meanings for sentence #1: A) At some time in the past, the time was 8:00 and the plane was in the process of arriving (continuing action) B) At some time in the past, the plane was expected to arrive at 8:00. C) Suppose it is now 9:00 and the plane has not yet arrived. The sentence could then mean that at some time in the past, the plane was expected to arrive at 8:00 but that expectation was wrong. D) At some time in the past, the usual arrival time was 8:00.

Good observation! In English, the past continuous tense ("was arriving") typically describes an action in progress over a period of time, rather than a momentary action. Since "arriving" is usually a momentary event rather than an ongoing action, it might seem odd to use the past continuous tense here. However, it’s not necessarily a mistake. Here’s why each sentence might still work in context: "The plane was arriving at eight." If the plane was approaching the airport and preparing to land, "was arriving" might imply the process of arrival rather than the exact landing moment. It could also mean the planned arrival time was at eight, so we’re viewing the approach as an ongoing event. "A tram was just arriving at the hill foot." Here, "was just arriving" could suggest that the tram was in the final part of its journey to the hill’s foot. This phrasing gives a sense of anticipation as it approaches, which might require a slight stretch of time, justifying the continuous tense. In both cases, "was arriving" can work if we think of "arrival" as a process with a little bit of duration, rather than a single instant.