4- ## Motion Analysis of a Ball: Velocity Vectors### (a) Construct Vectors with Lengths Proportional to the Horizontal and Vertical Velocities:The images below are motion diagrams based on a video analysis of a ball's path. The lengths of displacement and velocity vectors are proportional. Draw a series of vectors proportional to the average x and y velocity components during each 1/15th second interval. Begin with Frame 1 in each figure. Place the tail of the first velocity vector at the ball’s location in frame 1, then place the tail of the next vector at the ball’s location in frame 2, and so on.### Explanation of Figures:- **Figure 2**: Y-components of velocity - This graph shows the vertical velocity components of the ball over time. The vectors vary in length, indicating changes in vertical speed as the ball moves.- **Figure 3**: X-components of velocity - This graph illustrates the horizontal velocity components. The vectors are uniform in length, indicating a constant horizontal speed as the ball moves.### (b) Analysis**What happens to the x-component of the ball’s velocity, \(v_x\), as the ball moves horizontally?**- The \(v_x\) component remains constant, as shown by the uniform length of the vectors in Figure 3.**What happens to the \(v_y\) vectors? Explain how you arrived at your answers.**- The \(v_y\) vectors change in length, suggesting an increase or decrease in vertical speed. This indicates acceleration or deceleration due to gravity, as analyzed in Figure 2. The image presents two diagrams illustrating the velocity components in a fluid flow scenario. **Figure 2: Y-components of velocity**This diagram shows the Y-components (vertical components) of velocity in a flow field. It provides a visual representation of how the vertical velocity varies across the flow, marked by a series of dotted lines that indicate the velocity vectors at different points. The diagram implies a vertical assessment of flow dynamics, possibly through an obstruction or along a boundary.**Figure 3: X-components of velocity**This diagram depicts the X-components (horizontal components) of velocity in the same or a similar flow scenario. Similar to Figure 2, it uses dotted lines to indicate the velocity vectors, but these focus on the horizontal aspect of the flow. This figure highlights how the horizontal velocity changes across the flow, offering insights into how the flow might be influenced by factors such as barriers or gradients.Both figures are part of a study on fluid dynamics, aiming to clarify the differing roles of horizontal and vertical velocity components in various flow conditions.

Part (a): The required velocity vector at every 1/5th second can be drawn as, Where Vx is the…

(a) Construct Vectors with Lengths Proportional to the Horizontal and Vertical Velocities: The images that follow are motion diagrams created based on a video analysis of the ball's path. Use the fact that the lengths of displacement and velocity vectors are proportional to each other to draw a series of vectors that are proportional to the average xand y-velocity vector components during each 1/15th of a second time interval. Start with Frame 1 in each of the figures that follow. Place the tail of the first velocity vector at the ball's location in frame 1 and then place the tail of the next vector at the ball's location in frame 2 and so on.

(a) Construct Vectors with Lengths Proportional to the Horizontal and Vertical Velocities: The images that follow are motion diagrams created based on a video analysis of the ball's path. Use the fact that the lengths of displacement and velocity vectors are proportional to each other to draw a series of vectors that are proportional to the average xand y-velocity vector components during each 1/15th of a second time interval. Start with Frame 1 in each of the figures that follow. Place the tail of the first velocity vector at the ball's location in frame 1 and then place the tail of the next vector at the ball's location in frame 2 and so on.