Yes, that is called running extra fast. And then falling, with the same momentum. Unless there are two grounds, with different relativities. Like with a treadmill: you run relatively to the treadmill, but you are stationary relatively to the ground under it, because you run at exactly the same speed as the treadmill moves in the other way (hopefully for you…).
If the ground disappears from under your feet at 60 miles per hour, the moment you start falling are you falling at 60 miles per hour?
Yes, that is called running extra fast. And then falling, with the same momentum. Unless there are two grounds, with different relativities. Like with a treadmill: you run relatively to the treadmill, but you are stationary relatively to the ground under it, because you run at exactly the same speed as the treadmill moves in the other way (hopefully for you…).