Problem $6\mathrm{.}10$

You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface.

Sam, Amy, and Abigail are sliding on the horizontal surface and approaching at a point of the pond.

Sam, with mass $80\mathrm{.}0$ kg $,$ is given a push and slides eastward at $5\frac{m}{s}.$

Abigail, with mass $50\mathrm{.}0$ kg $,$ is sent sliding $3\frac{m}{s}$ northward.

They collide, and after the collision they stick together.

Problem $6\mathrm{.}10$

$($a$)$ What must be the initial velocity of Amy, with mass $60\mathrm{.}0$ kg $,$ if they are to end up moving at $7\frac{m}{s}30$ North of East after the collision?

$($b$)$ By how much did the total kinetic energy of the three people decrease during the collision?