A blue ball travelling at 2m/s collides with a red ball at rest on a table. After they collide, both balls move in the same direction. Both balls have the same mass. If the blue ball continues to move with a reduced velocity of 0.2m/s, what is the velocity of the red ball?
momentum is conserved
momentum lost by the blue ball is acquired by the red ball
To find the velocity of the red ball after the collision, we can make use of the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. Let's denote the mass of each ball as "m" and the initial velocity of the blue ball as "v1", and the final velocity of the blue ball as "v1f", and the initial velocity of the red ball as "v2" (which is 0 since it's at rest), and the final velocity of the red ball as "v2f". The principle of conservation of momentum can be expressed as:
(m * v1) + (m * v2) = (m * v1f) + (m * v2f)
Since both balls have the same mass, we can simplify the equation to:
v1 + v2 = v1f + v2f
Given that v1 = 2 m/s and v1f = 0.2 m/s, we can rearrange the equation to solve for v2f:
v2f = v1 + v2 - v1f
Substituting in the known values, we have:
v2f = 2 m/s + 0 m/s - 0.2 m/s
Simplifying, we find:
v2f = 1.8 m/s
Therefore, the velocity of the red ball after the collision is 1.8 m/s.