To predict the height of a ball after it has traveled a distance of 6.5 feet, we need more information about the trajectory of the ball. Several factors affect the height, including:

1. Initial velocity and angle of projection: This determines the initial kinetic energy and the direction of the ball’s motion.
2. Type of trajectory: Whether the motion is projectile motion, rolling, bouncing, etc.
3. Gravity, air resistance, and other forces: These will affect the motion of the ball.
4. Initial height: The starting position of the ball.

Assuming the ball is in projectile motion and neglecting air resistance, we can use the standard equations of physics. However, without specific values for initial velocity, launch angle, and initial height, it isn't possible to provide an accurate numerical prediction.

If you can provide the initial conditions or context of the situation, I can help with calculations or further insights!