Problem Eight. A space probe is launched from Earth. After a brief period of acceleration it moves at constant speed $0\mathrm{.}850$c relative to Earth. Batteries with a lifetime of $17\mathrm{.}0$ years $($in the probe$$s rest frame$)$ keep a radio transmitter operating at all times. Note: $1$ light$-$year $=$ c $(1$ year$).($THIS IS AN EXAM QUESTION.$)15.$ How long $($in years$)$ do the batteries last as measured from Earth? $($A$)14\mathrm{.}4($B$)27\mathrm{.}4($C$)32\mathrm{.}3($D$)43\mathrm{.}7($E$)57\mathrm{.}216.$ How far is the probe from Earth $($in light years$)$ when the batteries fail, as measured from the earth? $($A$)14\mathrm{.}4($B$)27\mathrm{.}4($C$)32\mathrm{.}3($D$)43\mathrm{.}7($E$)57.$