Gekkoukan High School features several clubs and activities for students, which are key to completing quests and forming social links necessary to fuse greater demons. One club that you will often hear about but never see is the Archery Club. Yukari, one of your demon-hunting teammates, will often mention having archery practice, but you'll never know where she runs off to. When you finally are tasked with asking the Archery Club for a favor, you will find that locating the club isn't about finding a room or a field but about finding the only known member: Yukari.
Enter the Velvet Room on April 30. The entrance to this room is located on the main floor of Tartarus to the left of the staircase. Once inside, speak with Elizabeth of competing quests.
Accept the quest for searching out the pine resin used by the Archery Club. You will be given until May 7 to complete this quest, which involves tracking down the club to obtain the necessary item.
Wait until the evening of May 2 to complete the quest. For the two days prior, you can continue to complete any other quest or press forward in your exploration of Tartarus.
Enter the common room on the first floor of your dormitory on the evening of May 2. You will find Yukari standing near the main seating area.
Speak with her, and you will learn that she is the only member of the Archery Club, and as such, she is the only one who can give you the pine resin. She will offer you the pine resin, which you can then add to your inventory.
Return to the Velvet Room before May 7, and speak with Elizabeth. Hand over the pine resin to complete the quest. You will receive two purifying rice items.
If you miss speaking to Yukari on May 7, restart the game from your last save to complete the quest.
These steps also apply to "Persona 3 Portable" on the PSP.
Archery Club is one of the few clubs you cannot join in "Persona 3," and your only contact with the club occurs at this point in the game.