These equations were derived from using d ⃗_y, the axis of symmetry, and a point on the parabola. It is necessary to have a known point on the parabola to determine the stretch of the parabola, defined as s. In the equations above let u define a point in vertical direction and h define a point in the horizontal direction. The point used in order to calculate the equation of the parabola that models the behaviour of a waltz jump was (1.61, 0). This point is used as 1.61m is where the skater lands on the ice, which is where the parabola model ends, and the ice is the horizontal plane defined as zero. Below h is defined as the horizontal distance, and u is the vertical distance. The math of figure skating spins:
A spin depicts circular motion. I wanted to investigate how the skater’s free leg affects the amplitude, and period of a cosine function. To analyze this I chose to video a figure skater doing a spin from a birds eye view, this way the points could be tracked all the way around the circle. If the video was taken facing the skater, many of the points on the cosine curve would be ‘hidden’ by the skater’s body. In figure 8, 9, and 10 show the different spins I chose to analyze.
Figure 8: Sit Spin Figure 9: Broken Leg Spin
Figure 10: Cross Foot On the figure above, the amplitudes are shown in a black line across the body. These were defined as the skaters’ amplitudes, because when measuring the amplitude of a circular motion object you measure from the
The leaping in the first revolution _{1u} is given by ((tR_{u})/2)-0 and the leaping in _{2u} is given by (((t+2)R_{u})/2)-((tR_{u})/2). Furthermore, the leaping in _{um_{u}} is given by ((R_{u}(t+m_{u}))/2)-((R_{u}(t+(m_{u}-1)))/2). Then, the distance L_{u} is given by:
In this lab we first created a scale to convert pixels to meters on the picture (71.03 pixels = 1 m). Using this scale we then determined the length from the top guy’s shoulders to feet (1.36m), the length of the right horizontal arm (.99m), and the length of the right horizontal arm (.94m). Next we took the inverse tangent of these terms to determine the angle made by the diagonal arms. (36.05° and 34.65°). We then took those terms to find the force felt by the diagonal arms, and their directions (79.16 kg @ 306.05° cartesian and 77.8 @ 235.35° cartesian). Next, using c^2 - a^2 = b^2 and those terms, we found the force felt by the horizontal arms - for their directions we used the cartesian grid (44.24 kg @ 180° cartesian and 46.59 kg @ 0°
Figure skaters’ VOR gain was 27% less than the control group during sinusoidal stimulation and the skaters’ responses are 10° phase advance when compared with the controls. VOR gain is 32% lower for the skaters’ during the velocity step, but there was no notable difference in the TC between the groups. The MS score is much lower for the skaters’ after vestibular stimulation (2.8+/-2.8 vs. 16.2 +/- 13.7). The findings were striking in the way that during the velocity step test the figure skaters’ gain is 32% lower than the control group. According to the researchers, this is quite significant. The figure skaters are much less likely to experience MS and VOR gain because of these findings. The results show that despite the young ages of the figure skaters, they are already showing signs of vestibular habituation. The hypothesis was generally supported because the VOR modifications seen in the skaters are in agreement with previous experiments on
The goal behind this experiment was to estimate the distance a ball would travel after it falls a certain distance and bounces off a metal plate which has an angle of 45 degrees. To find this we had to take the basic equations for kinematics which are (1/2)at2=x and v=v0+at and combine them to make an equation that will help us solve for the distance the ball will travel after hitting the bounce plate. The equation came out to be R=g*(sqrt(2)/sqrt(g))*(sqrt(H)*sqrt(h)), as that g is acceleration of gravity, h is the height of bounce plate, and H is the height of where the ball will be dropped. After completing this experiment the result was that the standard deviation was +/- 2.3 cmfrom the
The roots of the functions are what she will need to graph to see the parabola.
My methods of data collection to analyze my subject 's skill movement will consist of a multi-methods approach. This approach includes a mixture of literature reviews, observational review through video analysis, and interviews with the athlete. These data collection methods will help me in my project by allowing me to strategically point out differences in angular placement and posture, along with speed variations due to changes in position. I will be able to compare a professional style of skiing with that of a novice skier and point out the differences in positioning between an experienced skier and a novice skier. I will limit research information to scholarly and reputable sources only. Once of the sources I will reference comes from a research article called Clinical Biomechanics of Skiing.
This is freezing after the ball has left your hands because it will help take any spin
Many researchers are interested in the generation of angular momentum during turning dance movements. In a study on the pirouette en dehors, researchers found that skilled dancers generate larger vertical angular momentum as the number of turns increases by predominantly increasing the rate of momentum generation. Angular momentum is generated when the dancer applies a torque about the vertical axis by pushing sideways in opposite directions with both feet. The normal fourth position preparation is ideal for creating this angular momentum as the feet exert equal horizontal forces in opposite directions to produce the twisting effect, or torque (Kim et al., 2014). Thus, the vertical angular momentum is generated from the torque applied by the feet through the foot. In their book,
In tennis, it can be compared to topspin causing a ball to dip and backspin flattening the ball out. When the ball is hit off-center it causes the spinning effect. The speed and direction then determine the amount it curves during flight (Lees 1998). The curve of the ball while in the air can be known as the Magnus Effect. The Magnus can have both a negative and also a positive sign.
Writing the y-intercept in interval notation is [15/8,∞). The axis of symmetry has been found also which is where the x of the vertex is meaning that it is x=1/4. We will now find where does it increases and decreases, this should be easy now that we have our vertex and knowledge that all quadratic equations are parabolas. We know that the domain is (-∞,∞) any line coming from the negative side it will decrease while the positive side will increase. Then the side that is decreasing will stop to decrease at (-∞,1/4), it will then begin to increase at (1/4,∞). This time we are finding the x and y-intercept, beginning with the x-intercept we are going to use the discriminant of the quadratic equation which is b^2-4ac. Plugging the numbers, it will be (-1)^2-4(2)(2) the solution will be a negative fifteen. The rule of a discriminant is that there cannot be negative numbers for x, this time there are no x-intercept. the x-intercept does not exist we will replace it with a zero so the y-intercept can be found, by plugging the numbers y=2(0)^2-0+2 we will have the answer of y=2. The quadratic equation will be crossing the y-intercept at (0,2). Now writing the
Prompt #2: I personal don't have any experience when it comes to Magnus effect, because in High School I never played sports and the only sport I did was dance and cheerleading and technically the effect works better on balls or anything just rapidly spinning cylinder or sphere moving through air or another fluid in a direction at an angle to the axis of spin. I think I do have a clue on how I might use it in the future, but I'm not 100% sure yet. I know for a fact
This software assists in achieving the change in the position and determining the velocity. Once completed a plot was created to obtain a slope. The slopes on the graph are linear, and the points plotted fall on the line of best fit. The acceleration due to gravity for the free falling ball was measured to be 10.697 m/s^2 and 9.997 m/s^2 for the bouncing ball. The values are relatively close to the actual value of 9.8 m/s^2 . Once g values were obtained a percent error was calculated. For the free falling ball the error came out to 9.15% and percent error of the bouncing ball was 2.01%. Evidently from the percent errors there was not much error during the lab. Since there is a very small error it could have been from miss reading of the balls position or human error. Overall the lab was a success. The goal of measuring the acceleration due to gravity was achieved and the values received were relatively close. The predictions that a ball free falling would have negative velocity and then become even more negative and that a ball bouncing is expected to bounce up and have a positive velocity, then become negative were accurate and proved
Quadratic is the function that is used for a squared degree. In this function its graph is called a parabola. The graph of all quadratic function is called a parabola its shape is basically a U shape it might be transformed or reflected or inversed witch might change the shape in some cases
METHOD: An air hockey table was set up and a video camera on a tripod was placed over the air hockey table. The camera was positioned so it was directly above the air hockey table facing downwards. The air hockey table was turned on and two near identical pucks were placed on the table, one at one end of the table and one in the centre. The puck at the end of the table was launched by
On the graph above you can see that both the quadratic and the line are both adequate representations of the data collected by gold medalists for the men’s high jumps in the Olympics. Both of these lines follow the plots made on the original graph and they don’t stray too far from those lines either. There only outlier for the quadratic seem to be the medalist from the 1948 Olympics because his height is far below the quadratic. There might be some problems with the exact position of where the quadratic is and where the line is because they were drawn by hand and not on the computer like the stat plots which could potentially cause problems for interpreting the data.