A $75-$ kg

passenger on an amusement$-$park ride rotates around a $5-$ m

$-$diameter circular path with a constant speed of $5\mathrm{.}0$ m$/$s

$.($Figure $1)$ During the ride, an $8-$ kg

cushion fell vertically right into his hands from above, so he continued to rotate with it$.$ Then the cable supporting him is retracted until the diameter of his circular path is $3\mathrm{.}5$ m

$.$

Determine his resulting speed.

v

$=7\mathrm{.}90$ m$/$s

v

$=7\mathrm{.}14$ m$/$s

v

$=6\mathrm{.}45$ m$/$s

v

$=3\mathrm{.}87$ m$/$s