Ball A of mass 50 gm and speed 10 m/s colli | vedclass

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(D) Given: Mass of ball $A$,$m_A = 50 \ gm$; initial velocity of ball $A$,$u_A = 10 \ m/s$. Mass of ball $B$,$m_B = 10 \ gm$; initial velocity of ball

Vedclass · Accepted Answer

$\frac{85}{6} \ m/s$

Vedclass · Answer

(D) Given: Mass of ball $A$,$m_A = 50 \ gm$; initial velocity of ball $A$,$u_A = 10 \ m/s$. Mass of ball $B$,$m_B = 10 \ gm$; initial velocity of ball $B$,$u_B = -15 \ m/s$ (since it is moving in the opposite direction). Coefficient of restitution,$e = \frac{2}{5}$.The final velocity $v_B$ of the second ball $B$ after a one-dimensional collision is given by the formula:$v_B = \frac{m_A(1+e)}{m_A+m_B} u_A + \frac{m_B - e m_A}{m_A+m_B} u_B$Substituting the given values into the formula:$v_B = \frac{50(1 + \frac{2}{5})}{50 + 10} 	imes 10 + \frac{10 - (\frac{2}{5} 	imes 50)}{50 + 10} 	imes (-15)$$v_B = \frac{50 	imes \frac{7}{5}}{60} 	imes 10 + \frac{10 - 20}{60} 	imes (-15)$$v_B = \frac{70}{60} 	imes 10 + \frac{-10}{60} 	imes (-15)$$v_B = \frac{70}{6} + \frac{150}{60} = \frac{70}{6} + \frac{15}{6} = \frac{85}{6} \ m/s$Thus,the final speed of ball $B$ is $\frac{85}{6} \ m/s$.

Ball $A$ of mass $50 \ gm$ and speed $10 \ m/s$ collides with another ball $B$ of mass $10 \ gm$ and speed $15 \ m/s$ travelling in opposite directions. Determine the final speed of ball $B$,if the coefficient of restitution is $\frac{2}{5}$.

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