A 2-kg mass is moving in the positive x direction with speed of 3 m/s. A 3-kg mass is moving in the negative x direction with speed of 2 m/s. The two masses collide, and after the collision the 2-kg mass is moving in the negative x direction with speed of 3 m/s. a) What is the velocity of the 3-kg mass after the collision

Explanation:

First list the givens: (lets name the objects 1 and 2)

BEFORE COLLISION

1:

mass = 2kg

velocity = 3 m/s

Positive direction = ---> (moves to the right)

2:

mass = 3kg

velocity = -2 m/s

Negative direction = < (moves to the left)

AFTER COLLISION:

Since they bounce off each other, this is an elastic collision.

1:

mass = 2kg

velocity = -3 m/s

Negative direction < (moves to the left)

2:

mass = 3kg

velocity = ?

Positive direction > (moves to the right)

BEFORE COLLISION:

(1) >     <(2)

AFTER COLLISION:

(1) <  > (2)

Formula to find the velocity of 2 after the collision:

m1v1 + m2v2 = m1v1 + m2v2

(2kg)(3m/s) + (3kg)(-2m/s) = (2kg)(-3m/s) + (3kg)v2

6kgm/s + -6kgm/s = -6kgm/s + 3kgv2

0 = -6 + 3kgv2

Add 6 to the other side

6 = 3kgv2

Divide 3 to the other side

6/3 = 2

v2 = 2

The velocity to the 3kg mass is 2 m/s

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explanation: