Question

mr and mrs smith start at the same place and walk around a circular arena in opposite directions. mr smith walks with an angular speed of 1.1 x 10-3 rad/s, while mrs smith has an angular speed of 3.3 x 10-3 rad/s. how long will it be before they meet?

Answer 1

Mr. and Mrs. Smith's combined angular speed is 4.4 x 10^-3 rad/s. Since they walk around a circular path of 2π radians, it will take them approximately 1427.6 seconds to meet.

Step-by-step explanation:

The question involves finding the time before Mr. and Mrs. Smith meet while walking in opposite directions around a circular arena. To solve this, we need to find the combined angular speed of both Mr. and Mrs. Smith and then determine how long it takes for them to cover the full circumference of the circle (2π radians).

Mr. Smith's angular speed is given as 1.1 x 10-3 rad/s, and Mrs. Smith's angular speed is 3.3 x 10-3 rad/s. Since they are walking in opposite directions, their angular speeds add up. Thus, the combined angular speed is:

(1.1 x 10-3 + 3.3 x 10-3) rad/s = 4.4 x 10-3 rad/s.

Now, to calculate the time before they meet, we use the formula:

Time = Total Angle / Angular Speed

In this case, since they start from the same point and go around the circle until they meet, the total angle they cover is 2π radians (the full circle). The time is thus:

Time = 2π / (4.4 x 10-3)

Time ≈ 1427.6 seconds

Therefore, it will take approximately 1427.6 seconds or about 23.8 minutes for Mr. and Mrs. Smith to meet.