a large blue marble of mass 3.5 g is moving to the right with a velocity of 15 cm/s. the large marble hits a…

Explanation:

Step1: Apply conservation of momentum

The formula for conservation of momentum is $m_1u_1 + m_2u_2=m_1v_1 + m_2v_2$, where $m_1$ and $m_2$ are masses, $u_1$ and $u_2$ are initial - velocities, and $v_1$ and $v_2$ are final - velocities. Let $m_1 = 3.5\ g$, $u_1=15\ cm/s$, $m_2 = 1.2\ g$, $u_2 = 3.5\ cm/s$, and $v_1 = 5.5\ cm/s$. We need to find $v_2$. Substitute the values into the formula: $(3.5\times15)+(1.2\times3.5)=(3.5\times5.5)+(1.2\times v_2)$.

Step2: Calculate the left - hand side

$(3.5\times15)+(1.2\times3.5)=3.5\times(15 + 1.2)=3.5\times16.2 = 56.7$.

Step3: Calculate the right - hand side

$(3.5\times5.5)+(1.2\times v_2)=19.25+1.2v_2$.

Step4: Solve for $v_2$

Set the left - hand side equal to the right - hand side: $56.7=19.25 + 1.2v_2$. Subtract 19.25 from both sides: $1.2v_2=56.7 - 19.25=37.45$. Then $v_2=\frac{37.45}{1.2}\approx31\ cm/s$.

Answer:

31 cm/s