physics question. please no rounding. I need exact answer thanks!?

Question

A 6.0 g coin sliding to the right at 20.0 cm/s makes an elastic head-on collison with a 12.4 g coin that is initially at rest. After the collision, the 6.0 g coin moves to the left at 11.0 cm/s.
(a) Find the final velocity of the other coin.
(b) Find the amount of kinetic energy transferred to the 12.4 g coin.

Answer 1

6*20=12.4*v-6*11

solve for v
v=15 cm/s


The KE transferred is
.5*12.4*v^2
convert cm/s to m/s
and g to kg

KE=0.0001395 J

Actually, the problem as stated does not meet both conservation of energy and conservation of momentum. The resultant energy is HIGHER than the starting KE of the 6 g coin. Where did the energy come from?

Assuming an elastic collision, the collision actually produces a different outcome which will not satisfy the conditions as stated.

The solution that works is
the 6g coin moves at 6.957 cm/s to the left
and the 12.4 g coin moves at 13.04347826 cm/s to the right, not 11 as stated.


j