The centres of the spheres 1,2 and 3 lie on a single straight line. Sphere 1 is moving with an (...

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The centres of the spheres 1,2 and 3 lie on a single straight line. Sphere 1 is moving with an (initial) velocity \( v_{1} \) directed along this line and hits sphere 2 . Sphere 2, acquiring after collision a velocity \( v_{2} \), hits sphere 3 . Both collisions are absolutely elastic. What must be the mass of sphere 2 (in kg) for the sphere 3 to acquire maximum velocity (The masses \( m_{1} \) and \( m_{2} \) of spheres 1 and 3 are \( 9 \mathrm{~kg} \) and \( 1 \mathrm{~kg} \) respectively)?
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