A 4.00 kg mass is moving at 4.00 m/s 45.0 degrees NORTH of WEST and a 6.00 kg mass is moving at 3.00 m/s 30.0 degrees SOUTH of EAST. Find the velocity of the center of mass, letting (a) = the east-west component, and (b) = the north-south component.
A) a = 0.427 m/s, b = 2.31 m/s.
B) a = 1.23 m/s, b = 0.231 m/s.
C) a = 0.427 m/s, b = 0.231 m/s.
D) a = 1.73 m/s, b = 1.43 m/s.
E) a = 0.427 m/s, b = 0.213 m/s.

Question

Quizplus · Accepted Answer

To find the velocity of the center of mass, we need to use the formula:
velocity of center of mass = (m1v1 + m2v2) / (m1 + m2)

First, we need to find the components of the velocities in the x and y directions:

For the 4.00 kg mass:
vx1 = 4.00 m/s cos(45°) = 2.83 m/s (westward)
vy1 = 4.00 m/s sin(45°) = 2.83 m/s (northward)

For the 6.00 kg mass:
vx2 = 3.00 m/s cos(150°) = -2.60 m/s (eastward)
vy2 = 3.00 m/s sin(150°) = -1.50 m/s (southward)

Now, we can plug these values into the formula:
velocity of center of mass = (m1v1 + m2v2) / (m1 + m2)
= (4.00 kg)(2.83 m/s) + (6.00 kg)(-2.60 m/s) / (4.00 kg + 6.00 kg)
= -2.84 kg⋅m/s / 10.00 kg ≈ -0.284 m/s (eastward component)

= (4.00 kg)(2.83 m/s) + (6.00 kg)(-1.50 m/s) / (4.00 kg + 6.00 kg)
= 8.80 kg⋅m/s / 10.00 kg = 0.880 m/s (northward component)

Therefore, the velocity of the center of mass is approximately (0.284 m/s eastward, 0.880 m/s northward), or (a) = 0.284 m/s and (b) = 0.880 m/s. The closest choice to these values is C.

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