Question

A marble going at a speed of 2 m/s hits
another marble of equal mass at rest. If the collision is perfectly elastic,then the velocity of the first after collision is

Answer 1

Explanation:

Initial Momentum is equal to Final Momentum,

$(m1)(u1) + (m2)(u2) = (m1)(v1) + (m2)(v2)\\\\(m)(2) + (m)(0) = (m)(v1) + (m)(v2)\\\\2m = m(v1+v2)\\\\v1 + v2 = 2 ................................Equation 1$

Initial Kinetic Energy is equal to Final Kinetic Energy,

$\frac{1}{2}(m1)(u1)^{2}  + \frac{1}{2}(m2)(u2)^{2}   = \frac{1}{2}(m1)(v1)^{2}   + \frac{1}{2}(m2)(v2)^{2} \\\\\frac{1}{2}(m)(2)^{2}  + \frac{1}{2}(m)(0)^{2}   = \frac{1}{2}(m)(v1)^{2}   + \frac{1}{2}(m)(v2)^{2}\\\\4 + 0 = \frac{(v1)^{2}}{2} + \frac{(v2)^{2}}{2}\\(v1)^{2} + (v2)^{2} = 8 .............................................Equation 2$

Solving Equation 1 and 2 we will get velocity of first ball after collision.