Two people start at the same place and walk around a circular lake in opposite directions. One has an angular speed of 1.2 10-3 rad/s, while the other has an angular speed of 3.4 10-3 rad/s. How long will it be before they meet?
time=2PIrad/(1.2E-2 +3.4E-3)rad/sec
Both together transverse 2PI radians.
To find out 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 equal to the sum of the angular speeds of the two people. In this case, it is given as (1.2 × 10^(-3) rad/s) + (3.4 × 10^(-3) rad/s).
We can calculate the time it will take for them to meet by dividing the total angular displacement of the circle by the relative angular speed.
The total angular displacement of the circle is 2π radians because it is a complete revolution.
So, the time it will take for them to meet is given by:
Time = (Total angular displacement) / (Relative angular speed)
= 2π / ((1.2 × 10^(-3) rad/s) + (3.4 × 10^(-3) rad/s))
Let's calculate the time:
Time = 2π / (1.2 × 10^(-3) rad/s + 3.4 × 10^(-3) rad/s)
Time = 2π / (4.6 × 10^(-3) rad/s)
Time ≈ 1371.98 seconds
Therefore, it will take approximately 1371.98 seconds (or about 22 minutes and 51 seconds) for the two people to meet.
To find the time it takes for the two people to meet, we first need to determine the time it takes for each person to complete one full revolution around the lake.
Let's call the angular speed of the first person, ω₁, and the angular speed of the second person, ω₂.
The time it takes for one revolution is given by the formula:
Time = (2π) / ω
where ω represents angular speed.
For the first person, the time taken for one revolution is:
Time₁ = (2π) / ω₁
Similarly, for the second person, the time taken for one revolution is:
Time₂ = (2π) / ω₂
Since the two people are starting at the same place and walking in opposite directions, they will meet when the sum of their times taken for one revolution is equal to the same time.
Thus, we can set up the equation:
Time₁ + Time₂ = Time
Now we can substitute the values given in the problem:
Time₁ = (2π) / (1.2 × 10⁻³) rad/s
Time₂ = (2π) / (3.4 × 10⁻³) rad/s
Substituting these values into the equation, we have:
(2π) / (1.2 × 10⁻³) + (2π) / (3.4 × 10⁻³) = Time
Now we can calculate the time it takes for the two people to meet by evaluating this equation.