My Mom's property is host to a flock of wild turkeys, and I have witnessed their jumps first hand. We used to have a flat-top bird feeder on a pole (had to get rid of it when black bears started using it as a snack bar), and the turkeys would sometimes show up to pick at the seed that smaller birds knocked out and/or pick at the barberries that grow near the house.
During one particularly snowy winter, when I guess scratching in the woods was hard, I saw a turkey hen actually do a ground-level standing jump over 6' straight up and land on the flat top of the bird feeder. She then craned her neck around and flailed at the seed, getting some for herself and sending most of the feeder contents onto the snow for the rest of the flock. It was an impressive sight. When our phone rang, they ALL took off in a great flurry of feathers and scattered seed. Those things can go FAST.