A $2\mathrm{.}0$ g particle moving at$7\mathrm{.}4$m$/$s makes a perfectly elastic head$-$on collision with a resting$1\mathrm{.}0$ g$$object$.$

$($a$)$

Find the speed $($in m$/$s$)$ of each particle after the collision.

$2\mathrm{.}0$ g particle$$m$/$s$1\mathrm{.}0$ g particle$$m$/$s

$($b$)$

Find the speed $($in m$/$s$)$ of each particle after the collision if the stationary particle has a mass of$10$ g$.$

$2\mathrm{.}0$ g particle$$

Apply momentum conservation and assume a head$-$on elastic collision to find the final velocities from the initial velocities.$$m$/$s$1\mathrm{.}0$ g particle$$

Apply momentum conservation and assume a head$-$on elastic collision to find the final velocities from the initial velocities.$$m$/$s

$($c$)$

Find the final kinetic energy $($in J$)$ of the incident $2\mathrm{.}0$ g particle in the situations described in$$parts $($a$)$and $($b$).$

KE in part $($a$)$JKE in part $($b$)$

J

In which case does the incident particle lose more kinetic energy?

case $($a$)$case $($b$)$