Question

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?

Answer 1

L = - 1361.591 k Kgm/s

Step-by-step explanation:

Given

mA = 55.2 Kg

vA = 3.45 m/s

rA = 6.00 m

mB = 62.4 Kg

vB = 4.23 m/s

rB = 3.00 m

mC = 72.1 Kg

vC = 4.75 m/s

rC = - 5.00 m

then we apply the equation

L = (mv x r)

⇒ LA = mA*vA x rA = 55.2 *(3.45 i)x(6 j) = (1142.64 k) Kgm/s

⇒ LB = mB*vB x rB = 62.4 *(4.23 j)x(3 i) = (- 791.856 k) Kgm/s

⇒ LC = mC*vC x rC = 72.1 *(- 4.75 j)x(- 5 i) = (- 1712.375 k) Kgm/s

Finally, the total counterclockwise angular momentum of the three joggers about the origin is

L = LA + LB + LC = (1142.64 - 791.856 -1712.375) k Kgm/s

L = - 1361.591 k Kgm/s