Kate Middleton and Prince William visit Vernon Park, Nottingham, England on June 13, 2012. Credit: Stephen Lock/iImages/Polaris

Kate Middleton can't resist a little good-natured competition!

Attending one of her final Royal Jubilee tour obligations with Prince William by her side Wednesday in Nottingham's Vernon Park, the 30-year-old Duchess (a field hockey champ during her high school days) threw a rocket-shaped foam javelin when visiting with local schoolchildren.

William, 29, also tried his hand at launching the foam rocket -- and was able to land it five feet past his wife's best attempt.

During the outing, Middleton -- who donned her favorite blue Missoni coat -- used a parachute to pass a ball around and joined in a race to put up a tent.

Arranged by the Fields in Trust project, the athletic field day helped raise awareness for the Queen Elizabeth II Fields Challenge, of which William is a patron. The Challenge hopes to create 2,012 athletic fields in Britain by the end of December.

Wednesday's activities capped off a banner day for Middleton and William, who helped Queen Elizabeth wrap up her Jubilee tour, which began in March and marked 60 years of her reign.

For much, much more on William and Kate's private world -- their daily routines, her hair maintenance, whether Kate pays for her own clothes, William's romantic gestures -- pick up the new Us Weekly, on stands Friday!