# Multivariate Calculus: multivariate calculus – #27259

Question:

 . (a) A smooth sphere A of mass 6 kg, moving with speed 5 ms$^{-1}$ on a smooth horizontal surface, collides with another smooth sphere B of mass 3 kg, moving with speed 8 ms$^{-1}$. The velocities of A and B are inclined at angles ${{45}^{o}}$and ${{60}^{o}}$, respectively, anticlockwise to the line joining their centres at the moment of impact. Let the coefficient of restitution be $e=\frac{4}{5}$. Calculate the magnitudes and directions of the velocities of the spheres after impact. Work to 4 decimal places. [10]