Two people start at the same place and walk around a circular lake in opposite directions. One walks with an angular speed of 1.10 10-3 rad/s, while the other has an angular speed of 3.90 10-3 rad/s. How long will it be before they meet?

d1 + d2 = 2pi,

(1.1*10^-3)t + (3.9*10^-3)t = 2pi,
5*10^-3t = 2pi,
t = 2pi/0.005 = 6.28/0.005 = 1256 s =
20.9 min.

To determine how long it will take for the two people to meet, we can use the concept of relative angular speed.

The relative angular speed is the difference between the angular speeds of the two individuals. In this case, the relative angular speed is given by:

Relative Angular Speed = Angular Speed of Person 1 - Angular Speed of Person 2

Relative Angular Speed = 1.10 * 10^-3 rad/s - 3.90 * 10^-3 rad/s

Relative Angular Speed = -2.80 * 10^-3 rad/s

Since the relative angular speed is negative, it means that the two people are moving towards each other.

To find the time it takes for them to meet, we can use the formula:

Time = Angle / Relative Angular Speed

The angle here refers to the angular displacement between the two people when they meet. Since they are starting from the same place and walking in opposite directions, they will meet when the angular displacement between them sums up to a full circle (360 degrees or 2π radians).

Angle = 2π radians

Plugging in the values:

Time = 2π radians / (-2.80 * 10^-3 rad/s)

Calculating:

Time ≈ -6.28 * 10^3 s

Since time cannot be negative, it means that the two individuals have already met in the past. If they continue walking in their respective directions, they will meet again at regular intervals of approximately 6.28 * 10^3 seconds.