Question

Task 2
Using Center of Mass for Complex Motion
You’ve plotted and analyzed the Legs measurement for the snowboarder, but that may not be the most representative way to track the snowboarder’s position, velocity, and acceleration. He tucks his legs at the peak of the jump and then stretches them out below and in front of his path before he lands. He makes similar wild changes in position with his head, arms, and torso. No matter how his “parts” flail around, though, his center of mass should follow a projectile path. Tracker allows you to mathematically plot a center of mass point from other points on an object, even an object as complex as a human body.

To create the center of mass, you need to first use some more reference points for the snowboarder. Two additional reference points are already plotted for you: his head and back. They’ve just been “turned off” until now. Now you can use them with the Legs measurement to create an approximate center of mass measurement.

Reveal the hidden measurements:

In the top-left corner just above the video, click the blue arrow pointing down and select the Head measurement from the pop-up menu:

To the right of the blue arrow, the Legs measure selection has been replaced with “Head.” From the Head pop-up menu, select Visible:

Follow the same two-step process to make the Tail measure visible as well.
Next, Create a center of mass point:

Again, on the blue arrow pop-up, select Create Center of Mass.
From the Center of Mass “cm” dialog box, check all three measures: Legs, Tail, and Head. Then click the Create button. [Note: The mass of each of these three body sections has been estimated for you ahead of time (Legs = 30 kg., Tail = 40 kg., Head = 25 kg.). They add up to the snowboarder’s total mass of 95 kg.]
Move the coordinate axis to the center of the mass position at time t = 0.000 seconds. (Note that the coordinate axis is “angled” correctly. The video was shot at a slight angle.):
Set the table and the two graphs to display information for the cm point, if they don’t already do so.
Advance the video frame to time t = 0.000.
Click the origin of the axes and move it to the center of mass point, cm, near the center of the snowboarder’s body. You can drag the axes to move it quickly, but you can also use the arrow keys on a keyboard to adjust its position. Using the arrow keys (with the video at time = 0.000 sec), you should be able to get the cm readings in the table at t = 0.000 sec. to be very close to 0.000 meters for both x and y positions.
Finally, set the top plot for the cm readings to ax vs. t again and the bottom plot to ay vs. t.

Part A
Now play the video once again. Observe the graphs of the horizontal acceleration and vertical acceleration against time. How do the two graphs, ax vs. t and ay vs. t appear? What can you say about the acceleration of the snowboarder?

Part B
Now, change the two graphs to display the horizontal and vertical component of velocity versus time. What do you observe about the velocity components of the snowboarder, before and after time t = 0?

Part C
From the graph of the horizontal velocity against time, what can you say about the horizontal displacement of the snowboarder after time t = 0?

Part D
From your observations about the vertical velocity and acceleration, what can you say about the vertical displacement of the snowboarder after time t = 0?

Part E
Based on your analysis of the snowboarder’s motion, how do you think you could get even better results from a center of mass measurement like this one?

Answer 1

The concepts of launching projectiles of kinematics allow to find that the answers to the questions are:

    A) The accelleration ares: aₓ = 0 and  $a_y$ = - 9.8 m/s²

    B)  vₓ = v₀ and vertical velocity varies linearly with time

    C) The position is   x = vₓ t

    D)  The position y is   y = $v_{oy} \ t - \frac{1}{2} g t^2$  

    E)  Acceleration in the x axis due to friction.

After carefully reading your extensive writing, we can perform an analysis of the snowboarder's movement, as indicated by the analysts, it is performed on the point that represents the center of mass of the body.

Projectile launching is an application of kinematics to motion in two dimensions where in an x ​​direction there is not acceleration and in the y direction the acceleration is the gravity acceleration.

They indicate that the reference system is taken as the starting point of the exit point.

Let's analyze each part separately

Part A.

In projectile launch and video there is not acceleration on the x-axis, therefore

         aₓ = 0

Acceleration on the vertical axis is the gravity acceleration  

         y = - 9.8 m / s²

The negative sign indicates that the acceleration is directed downward.

Part B

Since there is no acceleration on the x axis, the velocity must be constant

            vₓ = v₀

In the vertical axis there is acceleration therefore the speed must change with time

           $v_y = v_{oy} - g t$

In other words, the speed must decrease, go through zero and continue in the negative as time increases.

Part C

The velocity on the x-axis is constant, therefore the position must increase with time linearly

              x = vₓ t

Part D

On the vertical axis there is an acceleration, therefore the velocity changes in time and the position is a quadratic function

              y = $v_{oy}$ t - ½ g t²

Part E

 The measurement regarding the mass center point is extremely useful since the complicated movement of the body parts is not taken into account.

One way to obtain better results is to include a small acceleration in the x axis due to friction.

In conclusion, using the concepts of launching projectiles of kinematics we can find the answers the questions are:

    A) The accelleration ares: aₓ = 0 and  $a_y$ = - 9.8 m/s²

    B)  vₓ = v₀ and vertical velocity varies linearly with time

    C) The position is   x = vₓ t

    D)  The position y is   y = $v_{oy} \ t - \frac{1}{2} g t^2$  

    E)  Acceleration in the x axis due to friction.

Learn more here:  brainly.com/question/10903823

Answer 2

Answer:

Part A.

In projectile launch and video there is not acceleration on the x-axis, therefore

        aₓ = 0

Acceleration on the vertical axis is the gravity acceleration  

        y = - 9.8 m / s²

The negative sign indicates that the acceleration is directed downward.

Part B

Since there is no acceleration on the x axis, the velocity must be constant

           vₓ = v₀

In the vertical axis there is acceleration therefore the speed must change with time

         

In other words, the speed must decrease, go through zero and continue in the negative as time increases.

Part C

The velocity on the x-axis is constant, therefore the position must increase with time linearly

             x = vₓ t

Part D

On the vertical axis there is an acceleration, therefore the velocity changes in time and the position is a quadratic function

             y =  t - ½ g t²

Part E

The measurement regarding the mass center point is extremely useful since the complicated movement of the body parts is not taken into account.

One way to obtain better results is to include a small acceleration in the x axis due to friction.

Explanation: