The Japanese sentence explained:
私たちは港市に向かっています。
watashitachi wa kooshi ni mukattaimasu.
We are sailing to the city.
| Japanese | Kana | Romaji | Explanation |
|---|---|---|---|
| 私たち | わたしたち | watashitachi | we |
| は | ・ | wa | (p.) topic/subject (actually ha but pronounced wa) |
| 港市 | こう・し | kooshi | city (specifically with a port / arbour) |
| に | ・ | ni | (p.) follows a word indicating a place where s.o./s.t. moves |
| 向かっています | むかっています | mukatteimasu | sailing |
(p.) stands for particle.
For the world city, I chose port city that is not exactly what Simple Sentence of the day states.
The verb 向かう (mukau) is an U verb. So, first, I have transformed it into TE-form 向かって (mukatte) as intermediate step before to obtain the progressive form (sail-ing) adding ~いる (a RU-verb). Afterward, I obtained from the RU-verb obtained in that way the polite form changing ~いる into ~います as for any RU-verb.
To better visualize it:
| 向か・う | mukau | (verb inf.) |
| 向か・って | mukatte | (TE-form of the verb) |
| 向か・って・いる | mukatteiru | (progressive form; also act like a normal RU-verb) |
| 向か・って・います | mukatteimasu | (polite form of the RU-verb) |
with the practice, this shall be done in a while for any U-verb 
.
EDIT:
向かう meaning is ‘to go towards’, ‘to head towards’.
To say “sailing” one of the choice can be to use:
- 航海 (‘sail’, ‘voyage’) and use the SURU-verb form 航海する （こう・かい・する）(kookai suru).
- The TE-form of a SURU-verb (an irregular verb) is 航海して （こう・かい・して）(kookai shite).
- The progressive form is obtained adding 〜いる 航海している （こう・かい・している）(kookai shite iru) where often the い is omitted as in 航海してる （こう・かい・してる）(kookai shite ru).
- The polite form would be 航海しています （こう・かい・しています）(kookai shite imasu).