Two people start at the same place and walk around a circular lake in opposite directions. One has an angular speed of 2.46 x 10-3 rad/s, while the other has an angular speed of 7.91 x 10-3 rad/s. How long will it be before they meet?
d1 + d2 = 2pi rads = A complete circle.
V1t + V2t = 2pi
2.46*10^-3 + 7.91*10^-3 = 6.28
10.37*10^-3t = 6.28
t = 606 s.
To find the time it will take for the two people to meet, we can use the concept of relative angular speed.
The relative angular speed is the sum of the angular speeds of the two people. In this case, the relative angular speed is (2.46 x 10^-3 rad/s + 7.91 x 10^-3 rad/s) = 10.37 x 10^-3 rad/s.
The time it will take for the two people to meet can be found by dividing the total angle covered by the relative angular speed. Since they are walking in opposite directions, they are effectively moving towards each other, which means they will meet when they have covered a total angle of 2π radians.
So, the time it will take is given by:
time = total angle / relative angular speed
time = 2π / (10.37 x 10^-3 rad/s)
To calculate this, we can use the following equation:
time = 2π / (10.37 x 10^-3) ≈ 608.64 seconds
Therefore, it will take approximately 608.64 seconds for the two people to meet.