A 1.0 kg red superball moving at 5.0 m/s collides head-on with stationary blue superball of mass 4.0 kg in an elastic collision. What are the final velocities of the two superballs after the collision?

Answer 1

In an elastic collision, both kinetic energy and momentum are conserved.
Let
m1=mass of red superball=1
m2=mass of blue superball=4
v11=initial velocity of red ball=5
v12=final velocity of red ball
v21=initial velocity of blue ball=0
v22=final velocity of blue ball

For conservation of energy,
(m1/2)v11² + (m2/2)v12&sup2 = (m1/2)v12² + (m2/2)v22².....(1)

For conservation of momentum,
(m1/2)v11 + (m2/2)v12 = (m1/2)v12 + (m2/2)v22 .......(2)

The only unknowns are v12 and v22. With the two equations, it is therefore possible to solve for the unknowns.

From (2), we express v12 in terms of the other unknown and the known constants, thus:
v12 = -(m2*v22-m2*v21-m1*v11)/m1

Substitute v12 into equation 1 will leave v22 as the only unknown.

Solving for v12 and v22, you should get
V12=-3 m/s, and v22=2 m/s.

Check that they satisfy the considerations of energy and momentum.

Answer 2

Note the following typographical corrections.

For conservation of energy,
(m1/2)v11² + (m2/2)v21² = (m1/2)v12² + (m2/2)v22².....(1)

For conservation of momentum,
m1 v11 + m2 v21 = m1 v12 + m2 v22 .......(2)
That is to say there is no need to divide the momentum by 2. Although this alone will not affect the final results.

Answer 3

tried solving it got different final results