A billiard ball rolling across a table at 1.45 m/s makes a head-on elastic colli

Question

A billiard ball rolling across a table at 1.45 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 initially at rest. 1st ball m/s 2nd ball m/s (b) The second ball is moving toward the first at a speed of1.20 m/s. 1st ball m/s 2nd ball m/s (c) The second ball is moving away from the first at a speed of0.80 m/s. 1st ball m/s 2nd ball m/s I already got the first 2. They were prettyeasy. The rest has stumped me. (a) The second ball is initially at rest. 1st ball m/s 2nd ball m/s (b) The second ball is moving toward the first at a speed of1.20 m/s. 1st ball m/s 2nd ball m/s (c) The second ball is moving away from the first at a speed of0.80 m/s. 1st ball m/s 2nd ball m/s I already got the first 2. They were prettyeasy. The rest has stumped me. 1st ball m/s 2nd ball m/s

Explanation / Answer

Given: -- m(1) = mass of ball 1 v(1) = vleocity of ball 1 m(2) = mass of ball 2 v(2) = velocity of ball 2 -- From conservation of momentum: -- m(1)*v(1)i + m(2)*v(2)i = m(1)*v(1)f + m(2)*v(2)f -- Since masses are the same, we have: -- v(1)i + v(2)i = v(1)f + v(2)f -- and -- v(1)i - v(1)f = v(2)f - v(2)i -- And from elastic head on collisions equations and somemanipulation, we can obtain: -- v(2)f = v(1)i -- and -- v(1)f = v(2)i -- so, Part (a): v(1)i = 1.40 m/s , v(2)i = 0 m/s v(1)f = 0 m/s , v(2)f = 1.40 m/s --->answer -- Part (b): v(1)i = 1.40 m/s , v(2)i = 1.15 m/s v(1)f = 1.15 m/s , v(2)f = 1.40 m/s --->answer -- Part (c): v(1)i = 1.40 m/s , v(2)i = 0.95 m/s v(1)f = 0.95 m/s , v(2)f = 1.40 m/s --->answer -- In head on elastic collisions, with equal masses, the objectsexchange velocities. -- Hope this helps. v(1)i = 1.40 m/s , v(2)i = 1.15 m/s v(1)f = 1.15 m/s , v(2)f = 1.40 m/s --->answer -- Part (c): v(1)i = 1.40 m/s , v(2)i = 0.95 m/s v(1)f = 0.95 m/s , v(2)f = 1.40 m/s --->answer -- In head on elastic collisions, with equal masses, the objectsexchange velocities. -- Hope this helps. v(1)i = 1.40 m/s , v(2)i = 0.95 m/s v(1)f = 0.95 m/s , v(2)f = 1.40 m/s --->answer -- In head on elastic collisions, with equal masses, the objectsexchange velocities. -- Hope this helps.

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