"Hurtle" is a verb meaning "move wildly at a dangerous speed". A car can hurtle down a street. Something can hurtle through the air.
"Hurdle" is first of all a noun, one of those fence-like objects that runners leap over. The word is also used figuratively, as in the sentence in question.
Originally hurdles were portable rectangular frames of woven wicker, used on farms as temporary gates or walls of sheep pens. As is typical with English nouns, a verb developed out of this meaning "jump over a hurdle".
Perhaps a way to remember that hurtle is spelled with a t is that if your car is hurtling down the street you are likely to get hurt.
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