"shoot down" is correct and usable in written English. You can use it when you want to indicate that something is rejected or negated. For example, "The boss shot down my proposal.".
"You don't just shoot down the plane".
Government aircraft would shoot down on them.
He then proceeds to shoot down the helicopter.
Powerful lasers might shoot down small pieces of debris.
"It could be used to shoot down an airplane.
When I feel like I can't trust my brain 100%, Ludwig really comes in handy. It makes me translate and proofread faster and my output more reliable.
Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu