Displacement and Time
The original data we collected involved the displacement, the time, and the angle at which the ball was hit. Collecting this involved three people. First, we measured the length of the court using the measuring tape. We then set the measuring tape in the middle of the court with the zero end on the baseline. I then went to the other baseline and hit the ball while one person recorded the time from when I hit it to when it landed, and the other measured the distance that it landed from the baseline. We performed this test 20 times, and then took the average of both the time and the distance from the baseline. Once we had these, we subtracted the distance from the baseline from the total length of the court to find the displacement of the ball. The average time was 1.22s, and the displacement after our calculations was determined to be 20.07m.
Initial Angle
To find the angle, we took rapid-fire pictures of the shot and drew a line from the contact point to the next closest location we had a picture of, and measured the angle to be about 18º.
Mass
To find the mass of the ball, we used a digital mass scale, which read 55g or 0.055kg.
Air Resistance
During our data collection, we made sure that air resistance was negligible. In order to do this, we took our measurements at an indoor tennis club. This ensured that there was no wind, and nothing else that could alter the speed of the ball in the air. Since air resistance was negligible, we do not need to take it into account when doing our calculations.
Maximum Height After Bounce
To find the maximum height of the ball off of the bounce, we used a visual reference from the pictures. At the maximum height, we saw that it was at the height of our helper's shoulders. We then measured the height of his shoulders and found that the maximum height of the bounce was 155cm.
Time The Ball Was on the Racquet
Finding the amount of time the ball is on the racquet for was a little bit challenging. I do not have a camera that is able to capture this, so I could not find the exact time of my shot. We did, however, find a slow motion video of a tennis shot, which was slowed down 100x. We then timed the amount of time the ball was on the racquet during this clip, and divided that number by 100 to get the actual time that the ball was on the racquet. The original time was around 0.4s, and divided by 100, that gives us 0.004s.
Distance The Ball Traveled on the Racquet
To find the distance that the ball was on the racquet for,
we looked took a close up video of the shot, and saw that it was on the racquet
for around the width of my shoe. After measuring my shoe, I was able to
determine that the distance the ball was on the racquet was 0.09m.
Coefficient of Friction
Finding the coefficient of friction was the hardest thing to find. Luckily, the International Tennis Federation (ITF) uses the coefficient of friction between a court and the tennis ball in their court pace ratings. Therefore, using their data, I was able to find the coefficient of friction of the court, since I knew the type of court we were using, which was 0.65.
Once we had all our data, we were ready to start doing our calculations.
*Note: this is just to give a general idea of the trajectory the ball took. This shot does not represent the average between all the shots, however it does give a good idea about what the shot looked like as it was the closest one to the data we used that we got pictures of. Also, this is not the court where the original data was collected, as if it were, we would have needed to take into account air resistance.