Solution to problem 7.4.14 from the collection of Kepe O.E.

Problem 7.4.14: Given the acceleration of the point a = 2ti + t2j. It is necessary to determine the angle in degrees between vector a and the Ox axis at time t = 1s. The acceleration of point a can be represented as a vector: a = 2ti + t^2j Then vector a at time t = 1s will be equal to: a = 21i + 1^2j = 2i + j The angle between vector a and the Ox axis can be found using the formula: cos(alpha) = (a, i) / |a||i| where alpha is the desired angle, (a, i) is the scalar product of vectors a and i, |a| and |i| - lengths of vectors a and i, respectively. Since vector i is codirectional with the Ox axis, then |i| = 1. Then: (a, i) = 2*1 + 0 = 2 |a| = sqrt((2)^2 + (1)^2) = sqrt(5) cos(alpha) = 2 / (sqrt(5)*1) = 2/sqrt(5) alpha = arccos(2/sqrt( 5)) ≈ 26.6° Answer: 26.6°.

Solution to problem 7.4.14 from the collection of Kepe O.?.

This digital product is a solution to problem 7.4.14 from the collection of Kepe O.?. in physics. The solution is presented in the form of a beautifully designed HTML page, which makes it easy to read and use.

In the problem it was necessary to determine the angle in degrees between the vector a and the Ox axis at the moment of time t = 1s, if the acceleration of the point a = 2ti + t2j is given. The solution contains a detailed algorithm for solving the problem, formulas, graphic diagrams and the answer accurate to tenths.

By purchasing this digital product, you gain access to useful information that will help you better understand physical laws and principles, and you will also be able to use the solution to this problem for your educational or professional purposes.

The digital product you are purchasing contains the solution to problem 7.4.14 from the collection by Kepe O.?. in physics. In the problem it was necessary to determine the angle in degrees between the vector a and the Ox axis at the moment of time t = 1s, if the acceleration of the point a = 2ti + t^2j is given. The solution is presented in a beautifully designed HTML page, making it easy to read and use.

The solution to this problem contains a detailed algorithm for solving it, formulas, graphical diagrams and the answer accurate to tenths. To find the angle between vector a and the Ox axis, the formula cos(alpha) = (a, i) / |a||i| was used, where alpha is the desired angle, (a, i) is the scalar product of vectors a and i, | a| and |i| - lengths of vectors a and i, respectively. Formulas were also used to find the length of the vector a and the value of the scalar product (a, i).

By purchasing this digital product, you get access to useful information that will help you better understand physical laws and principles, and you will also be able to use the solution to this problem for your educational or professional purposes.

***

Solution to problem 7.4.14 from the collection of Kepe O.?. consists in determining the angle between the acceleration vector of point a and the Ox axis at time t = 1s. To do this, you need to decompose the acceleration vector into components along the coordinate axes, and then use the formula to find the angle between the vectors:

cos(angle between vectors) = (a * i) / |a|

where a * i is the scalar product of vectors a and i (unit vector of the Ox axis), |a| - modulus of vector a.

In this case, the acceleration of the point is a = 2ti + t^2j. Substituting t = 1s, we get:

a = 2i + 1j

Thus, the expansion of the acceleration vector along the coordinate axes has the form:

a * i = 2 |a| = √(2^2 + 1^2) = √5

Substituting the obtained values ​​into the formula, we find:

cos(angle between vectors) = 2 / √5

Find the angle value using the arccosine trigonometric function:

angle between vectors = arccos(2 / √5) ≈ 26.6 degrees.

Thus, the answer to problem 7.4.14 from the collection of Kepe O.?. equal to 26.6 degrees.

***

1. A very convenient digital format, you can easily download and start using the solution to the problem.
2. Solution to problem 7.4.14 from the collection of Kepe O.E. in digital format allows you to save time searching for the desired page in the book.
3. Thanks to the digital format of the problem solution, you can easily copy and paste the solution into your report or document.
4. Excellent quality of images and formulas in digital problem solving.
5. The digital format of solving the problem allows you to quickly and conveniently check your answers.
6. The solution to problem 7.4.14 in digital format is available around the clock and can be used at any time and anywhere.
7. Convenient search by text and keywords in digital format for solving a problem allows you to quickly find the information you need.
8. The digital format of solving the problem allows you to save money on printing and delivering the book.
9. A very useful and informative digital product that helps you successfully solve physics problems.
10. A big plus of the digital format for solving a problem is the possibility of repeated use without wear and tear.