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Explanation: “...el aeroplano se fue directamente hacia arriba...”
The expression "straight" carries the connotation of a direct, unlingering action, which I believe, cannot be, in this case, separated from the accompanying preposition "up", which denotes a vertical or ascending direction..."directamente hacia arriba", and I tend to favor the expression "se fue" since thus, I don't have to explain, just as in your original text, if the plane was taking off or if it was maneuvering in the air.