$4.(8\mathrm{.}48)$ A $10\mathrm{.}0$ g marble slides to the left at a speed of $0\mathrm{.}400$ m$/$s on the

frictionless, horizontal surface of an icy New York sidewalk and has a

head$-$on$,$ elastic collision with a larger $30\mathrm{.}0$ g marble sliding to the right

at a speed of $0\mathrm{.}200$ m$/$s$.$

a$.$ Find the velocity of each marble $($magnitude and direction$)$ after

the collision. $($Since the collision is head$-$on$,$ all motion is along a

line.$)$

b$.$ Calculate the change in momentum $($the momentum after the collision minus the momentum before

the collision$)$ for each marble. Compare your values for each marble.$$

c$.$ Calculate the change in kinetic energy $($the kinetic energy after the collision minus the kinetic energy

before the collision$)$ for each marble. Compare your values for each marble.$$