3- **Projectile Motion Vectors**There are multiple ways to represent an object's motion. If the motion is two-dimensional and lies in a plane, some representations include:1. Recording x and y coordinates of the object at different times in a data table.2. Displaying the object's x and y locations at regular time intervals on a diagram.3. Drawing vectors (arrows) showing displacement, velocity, and acceleration and their x and y components at different times.4. Using vector equations to represent velocity and acceleration vectors quantitatively.The image on the right (Figure 1) is a motion diagram showing a ball’s location every 1/15th of a second as it rolls horizontally and then falls vertically for about 1 meter. The diagram visually represents the path and intervals of the ball’s motion.*Galileo Galilei, Dialogues Concerning Two New Sciences (Reprinted by Dover Publications)* **Transcription for Educational Website:****Motion Diagram Analysis**(d) The motion diagram in Figure 1 is a composite diagram constructed from a video analysis of the movie . The figure shows the position of the falling ball at equally spaced time intervals of 1/15th of a second (with t₂–t₁ = t₃–t₂ = t₄–t₃ and so on).**Explain why the relative lengths of the displacement vector components should also be proportional to the lengths of the corresponding velocity vector components that represent the average velocity during each time interval.***Note: The image or diagram referenced as Figure 1 is not provided here, but it is supposed to show the positions and vectors indicating the motion of a falling ball at specific intervals.*

The above motion consists of two motions one is horizontal motion ( motion with uniform linear velocity) and projectile motion. As the positions of the ball are captured after equal time intervals (∆t=15 s). The displacement vector in each time interval can be determined by multiplying the average velocity for a particular time interval with the time interval. The displacement can be determined as, ∆s→=V→avg∆t As the time interval is constant (∆t=15 s) hence the displacement will be proportional to the average velocity vector. When the ball is moving in a horizontal direction only, it is moving with uniform velocity and hence the average velocity for each interval will be equal hence the displacement vector for each interval, in this case, is the same. When the ball starts to fall back its horizontal velocity doesn't change, but the vertical component of velocity keeps on increasing (due to gravity) and hence the average velocity for each interval also keeps on increasing. Thus, for this interval, the displacement vector kept increasing with every passing time interval.

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Mechanical Engineering

(d) The motion diagram in Figure 1 is a composite diagram constructed from a video analysis of the movie .The figure shows the position of the falling ball at equally spaced time intervals of 1/15th of a second (with 2-1 = B-2 = 4-B and so on). Explain why the relative lengths of the displacement vector components should also be proportional to the lengths of the corresponding velocity vector components that represent the average velocity during each time interval.

(d) The motion diagram in Figure 1 is a composite diagram constructed from a video analysis of the movie .The figure shows the position of the falling ball at equally spaced time intervals of 1/15th of a second (with 2-1 = B-2 = 4-B and so on). Explain why the relative lengths of the displacement vector components should also be proportional to the lengths of the corresponding velocity vector components that represent the average velocity during each time interval.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

**Projectile Motion Vectors**

There are multiple ways to represent an object's motion. If the motion is two-dimensional and lies in a plane, some representations include:

1. Recording x and y coordinates of the object at different times in a data table.
2. Displaying the object's x and y locations at regular time intervals on a diagram.
3. Drawing vectors (arrows) showing displacement, velocity, and acceleration and their x and y components at different times.
4. Using vector equations to represent velocity and acceleration vectors quantitatively.

The image on the right (Figure 1) is a motion diagram showing a ball’s location every 1/15th of a second as it rolls horizontally and then falls vertically for about 1 meter. The diagram visually represents the path and intervals of the ball’s motion.

*Galileo Galilei, Dialogues Concerning Two New Sciences (Reprinted by Dover Publications)*

**Transcription for Educational Website:**

**Motion Diagram Analysis**

(d) The motion diagram in Figure 1 is a composite diagram constructed from a video analysis of the movie <Lab-2 Galileo Projectile 2.mov>. The figure shows the position of the falling ball at equally spaced time intervals of 1/15th of a second (with t₂–t₁ = t₃–t₂ = t₄–t₃ and so on).

**Explain why the relative lengths of the displacement vector components should also be proportional to the lengths of the corresponding velocity vector components that represent the average velocity during each time interval.**

*Note: The image or diagram referenced as Figure 1 is not provided here, but it is supposed to show the positions and vectors indicating the motion of a falling ball at specific intervals.*

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