Learn Russian: Мы спросим директора о проекте. - We will ask the director about the project.

Спросить is a perfective verb, which means it focuses on a single, completed result. Perfective verbs do not have a present tense! When you attach regular present tense endings (like -им for мы) onto a perfective verb, it automatically creates the simple future tense.

I learned the word for 'ask' is спрашивать. Why use спросим here?

Спрашивать is the imperfective verb, used for asking repeatedly, generally, or while an action is ongoing. Спросить is its perfective partner. Because we are talking about a single, specific completed action in the future (asking the director once), we use the perfective form спросим.

Why is it директора instead of just директор?

The director is the direct object of the verb, so the word must be in the accusative case. For masculine nouns that are living beings (animate), the accusative case looks exactly like the genitive case. We add an -а to the end, changing директор to директора.

Why is there an -е at the end of проекте?