Two objects of the same mass move along the same line in opposite directions. The first mass is moving with speed v. The objects collide, stick together, and move with speed 0.100v in the direction of the velocity of the first mass before the collision. What was the speed of the second mass before the collision

Answer: The velocity of the second mass is - 0.8*v

Explanation: This is a perfectly inelastic collision, where two objects that collide move together as if they were stuck to each other.

The final velocity in this type of collision is

Vf = (m1*v1 + m2*v2) / (m1 + m2)

Where the "m"'s are the masses of each object, and the v's are the velocities.

Here we know that m1 = m2 = m, v1 = v, Vf = 0.100*v

we want to find the value of v2

0.100*v = (m*v + m*v2) / (2m) = m (v + v2) / (2m) = (v + v2) / 2

0,100*v = v/2 + (v2) / 2

v (0.100 - 1/2) = (v2) / 2

-v*0.400*2 = v2

v2 = - v*0.8

Then we know that the second mass is moving with a velocity of - 0.8*v (the minus sign means that this object is moving in the opposite direction with respect to the other object)

One interesting thing in this type of collision is that the kinetic energy does not conserve