Crossword Genius

Be towed behind a boat, right in its wake, unfortunately (5-3)

Ross

I believe the answer is:

water-ski

I'm a little stuck... Click here to teach me more about this clue!

'be towed behind a boat' is the definition.
I can't tell whether this definition defines the answer.

'right in its wake unfortunately' is the wordplay.
'right' becomes 'r' (abbreviation).
'in' is an insertion indicator.
'unfortunately' indicates an anagram (a bad or unfortunate spelling).
'its'+'wake'='itswake'
'itswake' with letters rearranged gives 'wateski'.
'r' going within 'wateski' is 'WATER-SKI'.

Can you help me to learn more?

(Other definitions for water-ski that I've seen before include "Item used in aquatic sport" , "Aquatic sport accessory" , "Engage in aquatic sport" , "To ride behind a speedboat" , "Be towed behind a speedboat" .)

I've seen this clue in the Sydney Morning Herald.
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