A box slides down a $27\mathrm{.}0$ slope under its own weight. The coefficient of kinetic friction between the box and the slope is $0\mathrm{.}350.$ What is the acceleration of the box?

A$)1\mathrm{.}22\frac{m}{s^2}$

B$)1\mathrm{.}39\frac{m}{s^2}$

C$)2\mathrm{.}20\frac{m}{s^2}$

D$)2\mathrm{.}44\frac{m}{s^2}$

E$)2\mathrm{.}06\frac{m}{s^2}$

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$)9\mathrm{.}00$ m

C$)7\mathrm{.}50$ m

D$)5\mathrm{.}00$ m

E$)2\mathrm{.}50$ m

A pulley has an initial angular speed of $12\mathrm{.}5ra\frac{d}{s}$ and a constant angular acceleration of $3\mathrm{.}41ra\frac{d}{s^2}.$ Through what angle does the pulley turn in $5\mathrm{.}26$ s $?$

A$)160$ rad

B$)113$ rad

C$)19\mathrm{.}3$ rad

D$)22\mathrm{.}6$ rad

E$)42\mathrm{.}6$ rad

A pencil, $15\mathrm{.}7$ cm long, is released from a vertical position with the eraser end resting on a table. The eraser does not slip. Treat the pencil like a uniform rod. What is the angular speed of the pencil just before it hits the table?

A$)24\mathrm{.}5ra\frac{d}{s}$

B$)17\mathrm{.}2ra\frac{d}{s}$

C$)7\mathrm{.}23ra\frac{d}{s}$

D$)16\mathrm{.}8ra\frac{d}{s}$

E$)3\mathrm{.}70ra\frac{d}{s}$