$(($Please provide what formula to use in these following questions i will give you thumbs up$))$ Three masses are located in the $x-y$ plane as follows: a mass of $6$ kg is located at $(0m,0m),$a mass of $4$ kg is located at $(3m,0m),$ and a mass of $2$ kg is located at $(0m,3m).$ Where is the center of mass of the system?

A$.(1m,2m)$

B$.(2m,1m)$

C$.(1m,1m)$

D$.(1m,0\mathrm{.}5m)$

E$.(0\mathrm{.}5m,1m)$

Ans: D

$19.$ A $310-g$ air track cart is traveling at $1\mathrm{.}25\frac{m}{s}$ and a $260-g$ cart traveling in the opposite direction at $1\mathrm{.}33\frac{m}{s}.$ What is the speed of the center of mass of the two carts?

A$.2\mathrm{.}80\frac{m}{s}$

B$.0\mathrm{.}0732\frac{m}{s}$

C$.0\mathrm{.}131\frac{m}{s}$

D$.1\mathrm{.}47\frac{m}{s}$

E$.1\mathrm{.}29\frac{m}{s}$

Ans: B

$20.$ A $60\mathrm{.}0-kg$ man stands at one end of a $20\mathrm{.}0-kg$ uniform $10\mathrm{.}0-m$ long board. How far from the man is the center of mass of the man$-$board system?

A$.1\mathrm{.}25$ m

B$.2\mathrm{.}50$ m

C$.5\mathrm{.}00$ m

D$.7\mathrm{.}50$ m

E$.9\mathrm{.}00$ m

Ans: A

$21.$ A man is holding an $8\mathrm{.}00-kg$ vacuum cleaner at arm's length, a distance of $0\mathrm{.}550$ m from his shoulder. What is the torque on the shoulder joint if the arm is horizontal?

A$.0\mathrm{.}242$ Nm

B$.4\mathrm{.}40$ Nm

C$.43\mathrm{.}2$ Nm

D$.14\mathrm{.}5$ Nm

E$.0$ Nm

Ans: C