Ben, while the athlete in the first sentence is jumping, I would call it an adjective because it is describing the athlete. The hopping athlete might be right behind!
In the 2nd sentence, it's a verb because jumping is the action of the athlete.

Ben P.
Thank you, I also have a question on infinitives.
I have learned that infinitives can be used as adjectives, adverbs, and nouns. What part of speech is the bare infinitive jump when preceeded by a modal verb?
She can jump over the tallest hurdle.
...or the bare infinitive understand in this sentence below...
Dr. Smith spent the class period helping us understand problems.
Report
05/08/16

Ed M.
I must disagree that "infinitives can be used as adjectives, adverbs, and nouns." Infinitives, whether bare or
to-infinitives, are quintessentially verbs, unlike present and past participles derived from verbs which
can be used as adjectives and nouns.
So in She can jump over the tallest hurdle and Dr. Smith spent the class period helping us understand problems, both
jump and understand, respectively, are just verbs since, as you correctly identified these, they are bare infinitives. What might be confusing you especially is the second sentence where you have the present participle
helping followed close on its heels by understand; what's going on here is simply that the verb
help is subcategorized for (a fancy way of just saying "it takes") a so-called "small clause," that is, a string that kind of looks like a sentence, i.e., it has a "subject,"
us, but in the objective case because it functions as the direct object of
help (notice we couldn't say *helping we understand), a verb, here
understand which is in the infinitive rather than being a finite (conjugated) form since this is required of verbs in such "small clauses," and even a direct object of the verb,
problems, which incidentally proves that understand, despite being an uninflected infinitive, is still a legitimate (transitive) verb. And then
helping is in the -ing form because the verb spend is further subcategorized as taking a direct object (in this case
the class period) which may be followed by a "reduced clause" (remember I told you about those in my answer to your "whistling" question, which unfortunately I can't link to in this WyzAnt "Comment" box) featuring the present participle of a verb, a slot filled in this case by helping.
Report
05/09/16
Ben P.
Thanks again for explaining so well!
Report
05/09/16
Mark M.
05/08/16