How can I append json data in memory to the end of a new-line delimited json file without reading the file into memory in Rust?

Question

If I have a new-line delimited json file that looks something like this:

{"name":"butthead"}
{"name":"second-butthead"}
{"name":"third-butthead"}

And I have data loaded into memory that looks like this:

{"name":"fourth-butthead"}

How can I append the data I have in memory to the end of the json file without reading the json file into memory, using Rust, so that the json file ends like this:

{"name":"butthead"}
{"name":"second-butthead"}
{"name":"third-butthead"}
{"name":"fourth-butthead"}