Question

A billiard ball rolling across a table at 1.45 m/s makes a head-on elastic collision with an identical ball. Find the speed of each ball after the collision when each of the following occurs.

(a) The second ball is initially at rest.

first ball	m/s
second ball	m/s

(b) The second ball is moving toward the first at a speed of 1.10 m/s.

first ball	m/s
second ball	m/s

(c) The second ball is moving away from the first at a speed of 0.90 m/s.

first ball	m/s
second ball	m/s

Answer 1

During collision momentum is conserved

Initial momentum = Final momentum

Given that both balls are identical

--------(1)

===================

Since collision is elastic, kinetic energy is conserved

Initial kinetic energy = Final kinetic energy

Given that both balls are identical

-----------(2)

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(a) The second ball is initially at rest.

From (1)  

-----------(a)

--------

From (2)

Put (a) in the above equation

ANSWER:

Put the value of v₂ in (a)

ANSWER:

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(b) The second ball is moving toward the first at a speed of 1.10 m/s.

From (1)  

-----------(b)

--------

From (2)

Put (b) in the above equation

Solve the quadratic equation using a calculator

ANSWER:

Put the value of v₂ in (b)

ANSWER:

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(c) The second ball is moving away from the first at a speed of 0.90 m/s.

From (1)  

-----------(c)

--------

From (2)

Put (c) in the above equation

Solve the quadratic equation using a calculator

ANSWER:

Put the value of v₂ in (c)

ANSWER:

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