Hello!
Let's break down each option to figure out what's right/wrong about each:
An unusually strong cyclist can, it is hoped, provide enough power to set a new distance record for human-powered aircraft in MIT’s diaphanous construction of graphite fiber and plastic.
(A) can, it is hoped, provide enough power to set
This one is correct, so we'll leave it be for now.
(B) it is hoped, can provide enough power that will set
By not adding a comma between cyclist and it, we're saying the phrase "it is hoped" is essential to the meaning of the sentence. Since we know that's not true (you could remove it and the sentence would be fine), we know the punctuation is wrong here.
(C) hopefully can provide enough power, this will set
Adding a comma between power and this creates a comma splice. To fix this, one would have to replace that comma with a period, a semicolon, or reword it entirely. You cannot split apart two complete sentences with only a comma; it's not a strong enough break.
(D) is hopeful to set
This changes the meaning of the sentence. We're now saying the cyclist is the one who is hopeful to set a record, not the researchers involved in the study. Since we don't know who the cyclist is (saying "an unusually strong cyclist" suggests they haven't even chosen one yet), it's unlikely to know if the person is actually hopeful or not.
(E) hopes setting
Again, this suggests a cyclist who has not been chosen yet is already hopeful, which doesn't really make sense. Also, if you read this one out loud as they want you to write it, "hopes setting" doesn't work - it should be "hopes to set," or similar to how they worded it in D.
I hope this helps! I'm available if you need any follow up.
