There's definitely a cost: everything is type-erased and there's a lot more indirection than there would be if the code was compiled. But you usually don't hit performance issues because most app code (especially in the UI) is just a thin layer calling into the OS frameworks. The framework code does the heavy lifting and is all compiled.
The places you can hit performance issues are things like when the app itself has a tight loop that's doing a lot of work.
The places you can hit performance issues are things like when the app itself has a tight loop that's doing a lot of work.