Question

An 12.000 milligram particle is sliding across a friction-less one-dimensional path at 55.000 m/s and collides with a 68.000 milligram particle moving at -48.000 m/s in a perfectly inelastic collision. What are the velocities of the particles after the collision?

answer with correct units​

Answer 1

-3525.000 m/s

Step-by-step explanation:

In a perfectly inelastic collision, the two particles stick together and move with a common velocity after the collision. We can use the conservation of momentum to solve for this common velocity.

The initial momentum of the system is:

p_initial = m1 * v1 + m2 * v2

= (12.000 mg)(55.000 m/s) + (68.000 mg)(-48.000 m/s)

= -282.000 kg·m/s

Here, we convert the masses to kilograms to match the units of velocity.

Since the particles stick together after the collision, their masses add up:

m_final = m1 + m2

= 12.000 mg + 68.000 mg

= 80.000 mg

= 0.080 g

Now, we can use the conservation of momentum to find the final velocity:

p_final = m_final * v_final

where p_final = p_initial and m_final = 0.080 g.

Therefore:

v_final = p_final / m_final

= -282.000 kg·m/s / 0.080 g

= -3525.000 m/s