Three joggers are running along straight lines as follows: Jogger A, with a mass of 55.2kg, is traveling along the line y=6.00m at 3.45 m/s in the positive x-direction. Jogger B, with a mass of 62.4kg, is traveling at 4.23 m/s along the line x=3.00m in the positive y-direction. Jogger C, with a mass of 72.1kg, is traveling at 4.75 m/s along the line x=-5.00m in the negative y-direction. What is the total counterclockwise angular momentum of the three joggers about the origin?
To find the total counterclockwise angular momentum of the three joggers about the origin, we can calculate the angular momentum for each jogger separately and then add them together.
Angular momentum is given by the equation: L = mvr, where L is the angular momentum, m is the mass, v is the velocity, and r is the distance from the origin.
Let's calculate the angular momentum for each jogger:
For Jogger A:
Mass (m) = 55.2 kg
Velocity (v) = 3.45 m/s
Distance from the origin (r) = 6.00 m
Angular momentum for Jogger A (L_A) = m * v * r = (55.2 kg) * (3.45 m/s) * (6.00 m)
For Jogger B:
Mass (m) = 62.4 kg
Velocity (v) = 4.23 m/s
Distance from the origin (r) = 3.00 m
Angular momentum for Jogger B (L_B) = m * v * r = (62.4 kg) * (4.23 m/s) * (3.00 m)
For Jogger C:
Mass (m) = 72.1 kg
Velocity (v) = 4.75 m/s
Distance from the origin (r) = 5.00 m
Angular momentum for Jogger C (L_C) = m * v * r = (72.1 kg) * (4.75 m/s) * (5.00 m)
Now, we can calculate the total angular momentum by adding the individual angular momenta of the joggers:
Total angular momentum = L_A + L_B + L_C
That will give you the value of the total counterclockwise angular momentum of the three joggers about the origin.