A billiard ball rolling across a table at 1.75 m/s makes a head-on elastic colli

Question

A billiard ball rolling across a table at 1.75 m/s makes a head-on elastic collision with anidentical ball. Find the speed of each ball after the collisionwhen each of the following occurs.(a) The second ball is initiallyat rest. 1st ball Enter an exactnumber. 1 m/s 2nd ball Enter anumber. 2 m/s (b) The second ball is moving toward the first at a speed of1.20 m/s. 1st ball Enter anumber. 3 m/s 2nd ball Enter anumber. 4 m/s (c) The second ball is moving away from the first at a speed of1.00 m/s. 1st ball Enter anumber. 5 m/s 2nd ball Enter anumber. 6 m/s Enter an exactnumber. Enter anumber. Enter anumber. Enter anumber. Enter anumber. Enter anumber. 1st ball Enter an exactnumber. 1 m/s 2nd ball Enter anumber. 2 m/s

Explanation / Answer

(a)Let the mass and initial velocities of the two balls bem1,m2 and u1,u2respectively. The velocity of the two balls after the elastic collisionare v1 = [u1(m1 - m2)+ 2m2u2/(m1 + m2)]-----------(1) and v2 = [u2(m2 -m1) + 2m1u1/(m1 +m2)] -----------(2) where m1 = m2 and u1 = 1.70m/s,u2 = 0 m/s (b)When the second ball is moving toward the first at a speedof u2 = 1.00 m/s then we substitute u1 =1.70 m/s,u2 = -1.00 m/s in equation (1) and (2)respectively. (c)When the second ball is moving away from the first at aspeed of 0.90 m/s then wesubstitute  u1 = 1.70m/s,u2= +0.90 m/s in equation (1) and (2)respectively.

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