Question

What is the velocity of the 3 kg ball now?

Answer 1

2.333 m/s to the right

Step-by-step explanation:

By the conservation of momentum, we can write the following equation:

`\begin{gathered} p_i=p_f \\ m_1v_(1i)+m_2v_(i2)=m_1v_(1f)+m_2v_(2f) \end{gathered}`

Where m1 and m2 are the masses of the balls, vi, and vf are the initial and final velocities. If we take to the right as a positive and to the left as negative, we get

m1 = 2 kg

v1i = 3 m/s

m2 = 3 kg

v2i = -1 m/s

v1f = - 2 m/s

v2f = ?

Replacing the values and solving for v2f, we get:

`\begin{gathered} (2kg)(3m/s)+(3kg)(-1m/s)=(2kg)(-2m/s)+(3kg)v_(f2) \\ 6\text{ kg m/s}-3kg\text{ m/s = -4 }kg\text{ m/s + (3}kg)v_(f2) \\ 3kg\text{ m/s = -4 }kg\text{ m/s + (3}kg)v_(f2) \\ 3kg\text{ m/s + 4 }kg\text{ m/s = (3}kg)v_(f2) \\ 7kg\text{ m/s = (3}kg)v_(f2) \\ \frac{7\text{kg m/s}}{3kg}=v_(f2) \\ 2.333m/s=v_(f2) \end{gathered}`

Therefore, the velocity of the 3 kg ball is 2.333 m/s to the right.