Solution to problem 7.2.5 from the collection of Kepe O.E.

7.2.5 The speed of the point v = 2ti + 3j. Determine the angle in degrees between the velocity vector and the Ox axis at time t = 4 s. (Answer 20.6)

To solve the problem, we need to find the angle between the velocity vector and the Ox axis. To do this we use the formula:

cos α = (a · b) / (|a| |b|),

where α is the angle between vectors a and b, a · b is the scalar product of vectors a and b, |a| and |b| - lengths of vectors a and b, respectively.

In our case, the velocity vector is given as v = 2ti + 3j, and the Ox axis as i. Let's substitute the values ​​into the formula and solve it:

cos α = ((2ti + 3j) · i) / (|2ti + 3j| |i|) = (2t) / sqrt((2t)^2 + 3^2)

At t = 4 s we get:

cos α = (2*4)/sqrt((2*4)^2+3^2) ≈

Let's find the angle α through the inverse cosine:

α = acos(cos α) ≈ 20.6°

Thus, the angle between the velocity vector and the Ox axis at time t = 4 s is approximately 20.6 degrees.

Solution to problem 7.2.5 from the collection of Kepe O..

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Digital product "Solution to problem 7.2.5 from the collection of Kepe O.?." is a ready-made solution to a physical problem that can be used to prepare for exams, independently study material in physics, as well as for teaching students and schoolchildren.

Solving a problem includes a step-by-step description of the solution process, detailed calculations and an answer to the problem. The material is presented in an easy-to-read and understandable format with beautiful html design.

In this case, the task is to determine the angle in degrees between the velocity vector and the Ox axis at time t = 4 s. The solution to the problem is based on using a formula for finding the angle between vectors and substituting the corresponding values. The result of the solution: the angle between the velocity vector and the Ox axis at time t = 4 s is approximately 20.6 degrees.

Thus, by purchasing this digital product, you receive a ready-made solution to the problem that will help you successfully cope with physics problems and improve your knowledge and skills in this area.

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Problem 7.2.5 from the collection of Kepe O.?. consists in determining the angle between the point’s velocity vector and the Ox axis at time t = 4 seconds. According to the conditions of the problem, the speed of movement of a point is specified by the vector v = 2ti + 3j, where i and j are unit vectors along the Ox and Oy axes, respectively, and t is time in seconds.

To solve the problem, it is necessary to calculate the scalar product of the velocity vector and the unit vector directed along the Ox axis, and then apply the appropriate formula to find the angle between them. Substituting the velocity vector v and the unit vector i, we obtain:

v * i = (2ti + 3j) * i = 2ti * i + 3j * i = 2t * 1 + 3 * 0 = 2t

Here we use the property of the scalar product of vectors, according to which the product of a vector by a unit vector is equal to the projection of a given vector onto this unit vector.

Next, using the formula for calculating the angle between vectors through the scalar product, we get:

cos(angle) = (v * i) / (|v| * |i|) = (2t) / (sqrt((2t)^2 + 3^2) * 1) = (2t) / (sqrt(4t ^2 + 9))

Thus, the angle between the velocity vector and the Ox axis in degrees is equal to:

angle = arccos(cos(angle)) * 180 / pi = arccos((2t) / (sqrt(4t^2 + 9))) * 180 / pi

At time t = 4 seconds, substituting t = 4 into the expression for the angle, we get:

angle = arccos((2 * 4) / (sqrt(4 * 4^2 + 9))) * 180 / pi ≈ 20.6 degrees

Answer: the angle between the velocity vector and the Ox axis at time t = 4 seconds is approximately 20.6 degrees.

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