Coefficient of Restitution Calculation:

Given:
- Initial height (h) = 1 m
- Time interval between first and second impact (t) = 1.03 s

Formula:
The coefficient of restitution (e) can be calculated using the formula:

e = sqrt(h2 / h1)

Where:
- h2: Max height after the second impact
- h1: Initial height

Solution:

Step 1: Calculating the time taken to reach the max height after the first impact
Since the ball rebounds several times, it will reach the max height after each impact. The time taken to reach the max height can be calculated using the equation of motion:

h = ut + (1/2)gt^2

Where:
- u: Initial velocity (0 m/s as the ball is dropped)
- g: Acceleration due to gravity (9.8 m/s^2)
- t: Time taken to reach the max height

Rearranging the equation, we get:

t = sqrt(2h / g)

For the first impact, the time taken to reach the max height after the first impact (t1) is:

t1 = sqrt(2h / g) = sqrt(2 * 1 / 9.8) = 0.451 s

Step 2: Calculating the time taken to reach the max height after the second impact
The time interval between the first and second impact is given as 1.03 s. Therefore, the time taken to reach the max height after the second impact (t2) can be calculated as:

t2 = t1 + 1.03 = 0.451 + 1.03 = 1.481 s

Step 3: Calculating the max height after the second impact
Using the equation of motion, we can find the max height after the second impact:

h2 = ut2 + (1/2)gt2

Since the ball is dropped, the initial velocity (u) is 0 m/s.

h2 = (1/2)gt2 = (1/2) * 9.8 * (1.481)^2 = 10.886 m

Step 4: Calculating the coefficient of restitution
Using the formula:

e = sqrt(h2 / h1)

e = sqrt(10.886 / 1) = sqrt(10.886) = 3.296

Therefore, the coefficient of restitution is approximately 3.296.

Explanation:
The coefficient of restitution measures the elasticity of a collision between two objects. In this case, it represents the elasticity of the ball's collision with the floor. The coefficient of restitution is defined as the square root of the ratio of the maximum height reached after the collision to the initial height.

To calculate the coefficient of restitution, we first need to find the time taken to reach the maximum height after the first impact. Using the equation of motion, we find that the time taken is approximately 0.451 seconds.

Next, we calculate the time taken to reach the maximum height after the second impact by adding the given time interval (1.03 seconds) to the time taken after the first impact. This gives us a total time of approximately 1.481 seconds.