$($A$)$ Detail Workout Problems:

$(1)$ A $1\mathrm{.}00-$m$-$long ramp is inclined at $\backslash (15^\{\backslash$circ$\}\backslash )$ to the horizontal. A solid ball is released from rest at the top of the ramp. Find $($a$)$ the ball's speed at the bottom of the ramp and $($b$)$ its translational acceleration.

$(2)$ The Moon's rotation period is $27\mathrm{.}3$ days. What's the height of a "lunosynchronous" satellite that orbits the Moon, appearing fixed in the sky relative to a lunar observer? Compare your answer to the Moon's radius.