# AP Physics B Kinematics Presentation #66

TLDRThis video script explains the process of finding the magnitude of the sum of two vectors, A and B, with components (0, 1) and (-13, 0) respectively. The resultant vector C is obtained by adding the components of A and B, resulting in (-1, 4). To find the magnitude, the script uses the Pythagorean theorem, leading to the calculation of D as the square root of 17, which is approximately 4.1. The explanation also offers a method to approximate the answer without a calculator by comparing it to known squares, ensuring the answer is slightly greater than 4.

###### Takeaways

- ๐ The script discusses the process of adding two vectors, A and B, with components (0, 1) and (-13, 0) respectively.
- ๐ It explains that the sum of vectors A and B results in a new vector C with components (-13, 1).
- ๐ The magnitude of the sum, or the magnitude of vector C, is the focus of the question.
- ๐ The Pythagorean theorem is used to calculate the magnitude of a vector, which is the square root of the sum of the squares of its components.
- ๐งฎ The calculation involves squaring the x-component (-1) and the y-component (4) of vector C, resulting in the equation \( d^2 = 4^2 + (-1)^2 \).
- ๐ข Simplifying the equation gives \( d^2 = 16 + 1 \), which equals 17.
- ๐ The magnitude, D, is the square root of 17, which is approximately 4.1.
- ๐ซ The script suggests that if a calculator is not available, one can approximate the answer by knowing it must be greater than 4, since \( 4^2 = 16 \) and the square root of 17 is just a bit more.
- ๐ The script provides a method to narrow down choices without exact calculation by using known squares to estimate the range of the answer.
- ๐ The final answer is approximately 4.1, which is greater than 4 but less than the next whole number, indicating the magnitude of the vector sum.
- ๐ The script emphasizes the importance of understanding the process of vector addition and magnitude calculation even without the aid of a calculator.

###### Q & A

### What are the components of vector A?

-The components of vector A are 0 and 1.

### What are the components of vector B?

-The components of vector B are -1 and 3.

### How do you find the resultant vector C when adding vectors A and B?

-To find the resultant vector C, you add the corresponding components of vectors A and B. In this case, you add the x-components and the y-components of A and B.

### What is the x-component of the resultant vector C after adding vectors A and B?

-The x-component of the resultant vector C is -1, which is obtained by adding the x-component of A (0) and the x-component of B (-1).

### What is the y-component of the resultant vector C after adding vectors A and B?

-The y-component of the resultant vector C is 4, which is obtained by adding the y-component of A (1) and the y-component of B (3).

### What is the magnitude of a vector?

-The magnitude of a vector is its length or size, which can be found using the Pythagorean theorem if the vector is in two-dimensional space.

### How do you calculate the magnitude of the resultant vector C?

-To calculate the magnitude of the resultant vector C, you square the x-component, square the y-component, add the squares together, and then take the square root of the sum.

### What is the formula used to calculate the magnitude of the resultant vector C?

-The formula used is \( D^2 = (-1)^2 + 4^2 \), where D is the magnitude of the resultant vector C.

### What is the approximate magnitude of the resultant vector C without using a calculator?

-The approximate magnitude of the resultant vector C is about 4.1, based on the square root of 17.

### How can you estimate the magnitude of a vector without a calculator?

-You can estimate the magnitude by knowing the squares of numbers close to the actual values, such as knowing that 4 squared is 16 and then adding a little bit more for the square root of 17.

### Why is it important to know the range of possible magnitudes when estimating without a calculator?

-Knowing the range helps you to narrow down the choices and make an educated guess, especially when the exact calculation is not possible.

### What is the final answer for the magnitude of the resultant vector C as mentioned in the script?

-The final answer for the magnitude of the resultant vector C is approximately 4.1.

###### Outlines

##### ๐ Vector Addition and Magnitude Calculation

This paragraph explains the process of adding two vectors, A and B, with components (0, 1) and (-1, 4) respectively. The resultant vector C is obtained by adding the corresponding components of A and B, resulting in (-1, 4). The main focus of the paragraph is to determine the magnitude of vector C. The Pythagorean theorem is applied to calculate the magnitude, which involves squaring the x and y components, adding them together, and then taking the square root of the sum. The calculation leads to an approximate magnitude of 4.1, which is derived from the square root of 17. The paragraph also suggests a method to approximate the answer without a calculator by using known square values and logical deduction.

###### Mindmap

###### Keywords

##### ๐กVector

##### ๐กComponents

##### ๐กResultant Vector

##### ๐กMagnitude

##### ๐กPythagorean Theorem

##### ๐กSquare Root

##### ๐กApproximation

##### ๐กX Component

##### ๐กY Component

##### ๐กCalculation

##### ๐กEstimation

###### Highlights

Two vectors A and B have components (0, 1) and (-13, 0) respectively.

The sum of vectors A and B results in a resultant vector C.

To find the resultant vector C, add the X and Y components of A and B.

Vector C has components (-1, 4) after adding A and B.

The question asks for the magnitude of the sum of the two vectors.

The magnitude is found using the Pythagorean theorem.

The X component of vector C is -1 and the Y component is 4.

D^2 = 4^2 + (-1)^2 to calculate the magnitude using the Pythagorean theorem.

Solving for D gives D^2 = 16 + 1 = 17.

D is equal to the square root of 17.

The square root of 17 is approximately 4.1.

If no calculator is allowed, approximate the answer by knowing it must be greater than 4.

4^2 = 16, so taking the square root of 17 gives a value slightly more than 4.

The answer is approximately 4.1 without using a calculator.

You can narrow down choices by knowing the range should be around 4 and a little bit more.

Choices A, B, and C are not greater than 4, so D is the correct answer.

Use known squares to help approximate the solution without calculating the exact square root.

###### Transcripts

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