Chute

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early 19th century (originally a North American usage): from French, ‘fall’ (of water or rocks), from Old French cheoite, feminine past participle of cheoir ‘to fall’, from Latin cadere ; influenced by shoot.

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From French chute

Short for parachute.

etymonline

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chute (n.1)

1725, American English, "fall of water" (earlier shoot, 1610s), from French chute "fall," from Old French cheoite "a fall," fem. past participle of cheoir "to fall," from Latin cadere"to fall," from PIE root *kad- "to fall." Meaning "inclined tube, trough" is from 1804; that of "narrow passage for cattle, etc." first recorded 1871. In North America, absorbing some senses of similar-sounding shoot (n.1).

chute (n.2)

also 'chute, short for parachute (n.), attested from 1919.