Question

Две точки M и K движутся по окружности с постоянными угловыми скоростями 0,2 рад/с,0,3 рад/с. В начальный момент времени угол между радиусами этих точек равен Пи/3. В какой момент времени точки встретятся? ​

Answer 1

Ответ:t=5.23 c

Объяснение:

φ=φ2-φ1

π/6=ω2t-ω1t

дальше находим время

t=π/6(ω2-ω1)=π/6*0,1=5.23 c

здесь π=3.14

Answer 2

Problem Analysis

We have two points, M and K, moving along circles with constant angular velocities of 0.2 rad/s and 0.3 rad/s, respectively. The initial angle between the radii of these points is π/3. We need to determine at what moment in time the points will meet.

Solution

To find the moment when the points meet, we need to determine the time it takes for the angle between the radii to decrease to zero.

Let's assume that the initial position of point M is at angle θM and the initial position of point K is at angle θK. The angular positions of the points at any given time t can be calculated using the following equations:

θM = θM0 + ωMt θK = θK0 + ωKt

where: - θM0 and θK0 are the initial angles of points M and K, respectively. - ωM and ωK are the angular velocities of points M and K, respectively. - t is the time.

We want to find the time t when the angle between the radii is zero. In other words, we want to find the value of t for which the following equation is satisfied:

θM - θK = 0

Substituting the equations for θM and θK, we get:

(θM0 + ωMt) - (θK0 + ωKt) = 0

Simplifying the equation, we have:

(θM0 - θK0) + (ωM - ωK)t = 0

Now, we can solve for t:

t = (θK0 - θM0) / (ωM - ωK)

Substituting the given values: - θM0 - θK0 = π/3 - ωM = 0.2 rad/s - ωK = 0.3 rad/s

We can calculate the value of t.

Calculation

Let's calculate the value of t using the given values:

θM0 - θK0 = π/3 ωM = 0.2 rad/s ωK = 0.3 rad/s

t = (π/3) / (0.2 - 0.3) t = (π/3) / (-0.1) t = -π/30

Since time cannot be negative, we can ignore the negative sign. Therefore, the two points will meet at t = π/30 seconds.

Answer

The two points M and K will meet at t = π/30 seconds.

Note: The negative sign in the calculation is ignored because time cannot be negative.