[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
[tex]\underline{\mathbb{PROBLEM}:}[/tex]
- Two iceskaters stand together. They "push off" and travel directly away from each other, the boy with a velocity of [tex]\tt{\green{+ 1.50 \: m/s}}[/tex]. If the boy weighs [tex]\tt{\green{735.0 \: N }}[/tex] and the girl, [tex]\tt{\green{490 . 0 \:N }}[/tex] , what is the girl's velocity after they push off? (Consider the ice to be frictionless.)
[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
[tex]\underline{\mathbb{SOLUTION}:}[/tex]
» Remember that ;
» [tex]\sf{{W = mg }}[/tex], thus, [tex]\tt{{ \sf \: m = w/g.(use \: g = 9.8 \: m/ {s}^{2}) }}[/tex].
[tex]\sf{\qquad \qquad \: mass \: \qquad \qquad \: velocity} \\ \sf \qquad boy \qquad \green{75.00 \: kg }\qquad \qquad \green{1.50 \: m/s }\\ \sf \: { \: \: girl\qquad \green{50.00 \: kg}\qquad\qquad\qquad\green{?}}[/tex]
» The ice where they stand on is considered to be frictionless, thus, no external force is present. The momentum of the boy-girl system is conserved. There is no change in the momentum of the system before and after the push off.
[tex] \sf{Total \: Initial \: Momentum=Total \: Final \: Momentum} \\ \sf \: 0 = P_{\text{boy \: +}} \sf \: P_{\text{girl \:}} \\ \sf \: P_{\text{boy \: = }}P_{\text{girl \:}} \\ \sf \: \: (mv) _{\text{boy \: = }} \sf \: \: (mv) _{\text{girl \:}} \\ \sf \: \: 112.5 \: kg \: m/s = 50.0 \: kg \: (v_{\text{girl\: }}) \\ \: \: \: \: \: \: \: \: \begin{gathered} \begin{array}{l} \bold \therefore \boxed{ \green{{ \sf \: 2.25 \: m/s \: = V_{\text{girl }}}}}\Longleftarrow\textsf{Answer} \end{array} \end{gathered}[/tex]
[tex]\therefore[/tex]The girl moves with a velocity of [tex]\tt{\green{2.25 \: m/s }}[/tex] opposite to the direction of the boy.
[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
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