Answer
The speed of sphere A is $~~7.75~m/s$
The speed of sphere B is $~~3.87~m/s$
Work Step by Step
In part (a), we found that $U = 0.225~J$
Note that $~~m_B = 2m_A$
By conservation of momentum, the velocity $~~v_B = -\frac{v_A}{2}$
After a long time, the kinetic energy of the system will be equal to the initial electric potential energy since the electric potential energy will decrease to zero as the spheres move far apart.
We can find $v_A$:
$K = U$
$\frac{1}{2}m_A~v_A^2+\frac{1}{2}m_B~v_B^2 = U$
$\frac{1}{2}m_A~v_A^2+\frac{1}{2}(2m_A)~(-\frac{v_A}{2})^2 = U$
$\frac{1}{2}m_A~v_A^2+\frac{1}{4}m_A~v_A^2 = U$
$\frac{3}{4}m_A~v_A^2 = U$
$v_A^2 = \frac{4U}{3m_A}$
$v_A = \sqrt{\frac{4U}{3m_A}}$
$v_A = \sqrt{\frac{(4)(0.225~J)}{(3)(5.00\times 10^{-3}~kg)}}$
$v_A = 7.75~m/s$
We can find the velocity $v_B$:
$v_B = -\frac{v_A}{2}$
$v_B = -\frac{7.75}{2}$
$v_B = -3.87~m/s$
The speed of sphere A is $~~7.75~m/s$
The speed of sphere B is $~~3.87~m/s$
