A Utah family of saddle bronc riders will be profiled on Sunday’s edition of “60 Minutes” (6 p.m., KUTV-Channel 2).

The segment focuses on the Wrights, who the CBS newsmagazine calls “a cowboy clan holding on to a rein and a way of life.” Family members, who have called the Zion Wright Family Ranch in Virgin home for six generations, have “worked to become a dominant force in rodeo.”

CBS News correspondent Bill Whitaker traveled to southern Utah and to Las Vegas for the National Finals Rodeo for the report. And he expresses astonishment that the Wrights not only compete in saddle bronc riding — in which which riders try to hold on with one hand to a horse specially bred to buck them off — but that they’ve had so much success. At least one family member has made it to the national finals each of the past 15 years, and Cody Wright, 42, has won the event twice.

“It’s like one hell of a rocking horse,” Whitaker says.

“It can be the roughest ride in the world if you’re out of time, or it can be the smoothest ride in the world,” Cody Wright says. “I like to think you are [dancing with the horse]. I dance a lot better with a horse than I do my wife. I ain’t got no rhythm.”

The segment features both spectacular footage of southern Utah and walking wounded members of the Wright family. Three of them arrive for a group interview on crutches, and family members list injuries that include skull fractures, broken backs and brain bleeds. Jake Wright tells Whitaker he has broken his nose “about 10 times.”

The report also includes the next generation of Wright bronc rider. Viewers will see Cody Wright coaching his 16-year-old son, Statler, on his first bronc ride. The teenager says he was “super nervous until I got in there, and then I just pretty much forgot about everything else but what my dad’s taught me.” He was thrown after about 8 seconds and “hurt my butt, actually. But as soon as I hit the ground, I wanted to do it again.”