a piece of clay with mass m is traveling with an unknown velocity in the positive x-direction, when it collides and sticks to a block of mass 3m, moving with velocity v=-3m/s. after the collision, the block and clay are stuck together and traveling with a velocity of 1 m/s in the negative x-direction. what was the original velocity of the clay mass?

13 m in the + x direction.

Explanation:

Givens

m1 = m

m2 = 3m

v1= ? = x

v2 = - 3 m/s

v3 = v4 = - 1 m/s

Equation

Let x be the speed of the lighter object before collision.

Momentum before collision = momentum after collision

Solution

mx   - 3m * 3m/s = (m1 + m2)*(-1)

m(x - 3*3m/s) = (m + 3m)(-1)

m(x - 9) = - 4m                                      Cancel the ms

x - 9 = 4                                                 Add 9 to both sides

x = 9 + 4

x = 13 m/s