Farah fires Olympic home hopes with London win LONDON (Reuters) - World 5,000 meters champion Mo Farah underlined his credentials to become Britain's first Olympic long-distance gold medalist by winning his final warm-up in style at the London Grand Prix on Friday. Farah, who also won world silver in the 10,000 in Daegu last year, was confronted by a wall of sound from a bumper home crowd as he pulled away from Australia's Collis Birmingham on the final lap to win in 13 minutes, 6.04 seconds. It definitely went well, I'm definitely happy. Training's been going well so I'm looking forward to the Games," said Farah who crossed the line in his customary manner with arms outstretched as fireworks were set off from the roof of one of the stands. American Tyson Gay made a poor start in the men's 100 final but came through in the final 20 meters to win in a time of 10.03 into a headwind. "It felt pretty good just to get the victory and if the wind had been in our favor I think we all would have run under 10 seconds," said the 29-year-old. My groin is a little tender but it held up," added Gay, who had surgery on his right hip last year. In the absence of former world record holder Asafa Powell -- who pulled out of the meeting with a groin problem -- Ryan Bailey of the U.S. was second as Jamaica had to settle for third place with Nesta Carter. Gay said he could understand why Powell chose not to compete so close to the London Games, which start on July 27. I know what it's like to have a groin injury. I wish him all the best and a speedy recovery," he said. Injury problems also struck China's 2004 Olympic champion Liu Xiang who had to pull out of the final of 110 meters hurdles after tweaking his back while warming up. With Liu sidelined, world indoor champion Aries Merritt defied the cold, damp conditions with a dominant display to win in 12.93 and equal his world leading time. Britain's Perri Shakes-Drayton provided some early cheer for home fans, winning the women's 400 hurdles ahead of European champion Irina Davydova in a personal best of 53.77, a time that took her to second in the world this year. Beijing gold medalist Melaine Walker of Jamaica was fourth. "I know I'm doing the right thing with my coach so roll on the Olympics," Shakes-Drayton said. I'm very happy with today's performance. I wanted a season's best so I'm very happy," added the 23-year-old. World champion Dai Greene could not provide the crowd with a British double in the event as Puerto Rica's Javier Culson maintained his unbeaten record for the season, winning the men's 400 hurdles in 47.78 to equal his world leading time. Greene finished strongly to snatch second place ahead of Olympic champion Angelo Taylor in 48.10. I've got a few more weeks to get a bit sharper for the Olympics and I'm going in the right direction I think. So I'm looking forward to the Olympics and hopefully I can get one over Culson then," said Greene who narrowly lost to Culson in Paris last week. Kenyan double world champion Vivian Cheruiyot showed why she is a medal favorite at the Olympics by winning her 11th successive 5,000 meters race. Cheruiyot, who also plans to run the 10,000 in London, was shadowed by compatriot Mercy Cherono coming into the final bend but with a quick look over her shoulder, the world champion kicked again and pulled away to win by a meter. Pole vaulter Steve Hooker's problems continued after the Australian Olympic champion did not register a height, failing three times at 5.40 meters in the difficult conditions. Hooker has been battling psychological problems he compares to the "yips" golfers suffer and only cleared the qualifying height for the Olympics at a special event organized by his sponsor. It was not much better for Olympic favorite Renaud Lavillenie of France, whose only clearance was at 5.40. The event was won by Germany's world indoor silver medalist Bjorn Otto with a height of 5.74. American Chaunte Lowe won the women's high jump with a leap of 2.00 meters and Australian Mitchell Watt took the men's long jump with 8.28 meters, two centimeters further than Britain's Chris Tomlinson. Editing by Justin Palmer