Do they tell you what the statute says, or whether you're working with common law or the MPC? This is my take, but I'm still in the process of studying this stuff.
Poster above is correct. Under common law, there is no clear mens rea for rape - it's a general intent crime that probably implies knowingly or purposely having intercourse, but there is no required mens rea as to the element of the lack of consent. That part is strict liability. So unreasonable mistake of fact doesn't relieve liability, and neither does reasonable mistake. It seems like you'd need to know more about the actual facts to know whether or not the "by physical force" requirement was met, because that's how the common law gets around the question of whether this was a bad act without imposing a mens rea, since the common law is big on seeing the actus reus.
The MPC explicitly removes the consent element, and the resistance requirement, and says the intercourse must be "by force or by threat of imminent death, serious bodily injury, extreme pain or kidnapping." So under the MPC for it to be straight-up rape, you'd still need to show some kind of force or threat of force. It could be gross sexual imposition if there is a lesser threat that would prevent resistance by "a woman of ordinary resolution." Again, because the consent element is left out, there is no required mens rea either way as to the consent, so it just doesn't matter what the D thought, or whether he was reasonable in thinking it.
Some modern jurisidictions have kept the consent requirement and imposed or discussed imposing a mens rea on this element of the crime. However, if you only know that D was unreasonable in his mistake (negligent), and cannot show that he was aware of the risk of harm (reckless), his mens rea may not be sufficiently culpable to convict him of rape, because the MPC and many jurisdictions are hesitant to impose a mens rea of less than recklessness for criminal liability.
Someone correct me if I'm wrong! Very possible!
Were there any more facts included in your hypo? It seems like a difficult question unless you know what laws they want you to apply, and about the force, etc.