Question

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

Initial conditions:
m1 = 1.0 ; v1 = 5
m2 = 4.0 ; v2 = 0

In the case where the second object (sometimes called the target) is at rest the velocities after the condition are

v1' = v1* (m1-m2)/(m1+m2)
v2' =  2v1*m1/(m1+m2)

For this we get
v1' = 5*(-3)/5 = -3m/s  (moving in the opposite direction as before at 3m/s
v2' = 2*5*(1)/5 = 2m/s in the same direction as the original ball was moving
you can see these directions by looking at the signs.  The momenta also add to the initial momentum as required.

Answer 2

Answer:

final speed of blue ball = 2m/s

final speed of red ball = -3 m/s

Explanation:

As we know that for elastic type of collision the coefficient of elasticity is always 1 and it is given by

$e = \frac{v_2 - v_1}{u_1 - u_2}$

here we know that

$u_1 = 5 m/s$

$u_2 = 0$

now we have

$v_2 - v_1 = 5 - 0 = 5 m/s$

also we can use the momentum conservation for this type of collision

so we will have

$1\times 5 + 4 \times 0 = 1\times v_1 + 4 \times v_2$

so we have

$v_1 + 4v_2 = 5$

now from above two equations we will have

$5 v_2 = 10$

$v_2 = 2 m/s$

also we have

$v_1 = - 3m/s$

so final speed of blue ball = 2m/s

final speed of red ball = 3 m/s