To find the total distance traveled by a ball that bounces off the floor three times and then lands on another surface, we need to consider the distance covered during each bounce and the distance covered when the ball lands on the final surface.
Let's assume the ball's initial height above the floor is denoted by H and the coefficient of restitution (a measure of bounciness) is denoted by e. When the ball bounces, it will rebound to a certain height determined by the coefficient of restitution.
The distance traveled during each bounce is given by the formula: Distance = 2 * H * e
The first bounce covers a distance of 2 * H * e. After the first bounce, the ball reaches a certain height (let's call it H1) and then bounces again. The distance covered during the second bounce is 2 * H1 * e. Similarly, the third bounce covers a distance of 2 * H2 * e, where H2 is the height reached after the second bounce.
Finally, after the third bounce, the ball lands on another surface. The distance covered from the point of the third bounce to the final landing position will depend on the horizontal distance between the bounce point and the landing point.
To find the total distance traveled, we sum up the distances covered during each bounce and add the horizontal distance traveled after the third bounce.
Total Distance = (2 * H * e) + (2 * H1 * e) + (2 * H2 * e) + Horizontal Distance
Please note that the specific values of H, e, H1, H2, and the horizontal distance would be needed to calculate the total distance accurately.