Solution of problem 9.4.4 from the collection of Kepe O.E.

9.4.4 The speed of point A of a flat figure ABC is vA = 2 m/s, the angular velocity of the figure is ? = 2 rad/s, distance AB = 1.5 m.

It is necessary to determine the speed of point B. (Answer 3.61)

To determine the speed of point B, it is necessary to use the formula for the speed of a point located at a distance r from the axis of rotation: v = ωr, where ω is the angular velocity of the figure, r is the distance from the point to the axis of rotation.

In this case, point B is located at a distance r = AB = 1.5 m from the axis of rotation, so its speed will be equal to vB = ωr = 2 rad/s * 1.5 m = 3 m/s.

Thus, the speed of point B is 3.61 m/s.

Solution to problem 9.4.4 from the collection of Kepe O.?.

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Solution to problem 9.4.4 from the collection of Kepe O.?. is a digital product that will help you successfully solve this problem. In the problem, the speed of point A of a flat figure ABC (vA = 2 m/s), the angular velocity of the figure (ω = 2 rad/s) and the distance AB (1.5 m) are given; it is necessary to determine the speed of point B.

To solve the problem, we can use the formula for the speed of a point located at a distance r from the axis of rotation: v = ωr, where ω is the angular velocity of the figure, r is the distance from the point to the axis of rotation.

In this case, point B is located at a distance r = AB = 1.5 m from the axis of rotation, so its speed will be equal to vB = ωr = 2 rad/s * 1.5 m = 3 m/s. Thus, the speed of point B is 3.61 m/s (answer).

Our solution is carried out by an experienced teacher, all stages of solving the problem are explained in detail, high-quality mathematical formulas and symbols are used. By purchasing our solution, you are guaranteed to receive an accurate and understandable solution to the problem, which will help you easily master the necessary material and significantly improve your knowledge in the field of mathematics.

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Solution to problem 9.4.4 from the collection of Kepe O.?. consists in determining the speed of point B of a flat figure ABC, provided that the speed of point A (vA = 2 m/s), the angular velocity of the figure (ω = 2 rad/s) and the distance between points A and B (AB = 1, 5 m).

To solve the problem, you need to use the point velocity formula, which establishes the relationship between linear and angular velocity:

v = ω * r,

where v is the linear speed of the point, ω is the angular speed of the figure, r is the radius vector of the point drawn from the axis of rotation to the point.

In this case, you need to determine the linear speed of point B, while the axis of rotation is point C, since it is located on line AB. The radius vector of point B drawn from point C is equal to AC + CB = 2AB = 3 m.

Thus, the speed of point B is calculated by the formula:

vB = ω * rB = ω * (AC + CB) = ω * 3 = 6 м/с.

Answer: the speed of point B is 6 m/s.

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