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------------------------------------------------ A 1.70-kg particle has a velocity (1.50 î − 5.00 ĵ) m/s, and a

5.00-kg particle has a velocity (1.00 î + 7.00 ĵ) m/s. (a) Find the

velocity of the center of mass. î + ĵ m/s (b) Find the total

To find the velocity of the center of mass, we can use the formula:

V_cm = (m1 * v1 + m2 * v2) / (m1 + m2)

Where V_cm is the velocity of the center of mass, m1 and m2 are the masses of the particles, and v1 and v2 are their respective velocities.

Given:
Mass of particle 1 (m1) = 1.70 kg
Velocity of particle 1 (v1) = (1.50 î - 5.00 ĵ) m/s

Mass of particle 2 (m2) = 5.00 kg
Velocity of particle 2 (v2) = (1.00 î + 7.00 ĵ) m/s

Let's substitute these values into the formula:

V_cm = (1.70 kg * (1.50 î - 5.00 ĵ) m/s + 5.00 kg * (1.00 î + 7.00 ĵ) m/s) / (1.70 kg + 5.00 kg)

Simplifying the equation, we get:

V_cm = (1.70 kg * 1.50 î - 1.70 kg * 5.00 ĵ + 5.00 kg * 1.00 î + 5.00 kg * 7.00 ĵ) / (6.70 kg)

V_cm = (2.55 î - 8.50 ĵ + 5.00 î + 35.00 ĵ) / 6.70 kg

V_cm = (7.55 î + 26.50 ĵ) / 6.70 kg

Therefore, the velocity of the center of mass is 7.55 î + 26.50 ĵ m/s.

For part (b), to find the total mass, we simply add the masses of the particles:

Total mass = m1 + m2 = 1.70 kg + 5.00 kg = 6.70 kg.

So, the total mass is 6.70 kg.

I hope this helps! Let me know if you have any further questions.

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