Question

A 9.00 kg mass is moving to the right with a velocity of 14.0 m/s. A 12.0 kg mass is moving to the left with a velocity of 5.00 m/s. Assuming that these two balls have a head on collision and stick together, what will be the final velocity of the combination? (3.1 m/s)

Answer 1

5.95 m/s to the right

Step-by-step explanation:

Before the collision, the momentum of the system is given by:

p = m1v1 + m2v2

p = (9.00 kg)(14.0 m/s) + (12.0 kg)(-5.00 m/s)

p = 125.0 kg m/s (to the right)

During the collision, the two masses stick together, so their final velocity will be the same. Let's call this final velocity vf. The momentum of the system after the collision is given by:

p' = (m1 + m2)vf

p' = (9.00 kg + 12.0 kg)vf

p' = 21.0 kg vf

Since momentum is conserved in the collision (there are no external forces acting on the system), we can set p = p' and solve for vf:

125.0 kg m/s = 21.0 kg vf

vf = 5.95 m/s (to the right)

Therefore, the final velocity of the combined masses after the collision is 5.95 m/s to the right.