A blue ball travelling at 2m/s hits a red ball at rest on a table. after they collide both balls move in the same direction. Both balls have the same mass. The blue ball continues to move with a reduced velocity of 0.2m/s what is the velocity of the red ball?
answered
momentum before = momentum after
m * 2 + m * 0 = m * .2 + m * v
1.8 = v
To find the velocity of the red ball after the collision, we can use 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 (p) of an object is defined as the product of its mass (m) and velocity (v):
p = m * v
Since both balls have the same mass (m), we can assign the same value to them. Let's call it "m".
Before the collision, the blue ball has a velocity of 2 m/s. Since the red ball is at rest, its velocity is 0 m/s.
The total initial momentum of the system is given by:
p_initial = m * v_blue + m * v_red
= m * 2 + m * 0
= 2m
After the collision, both balls move in the same direction with the blue ball having a velocity of 0.2 m/s. Let's call the velocity of the red ball after the collision "V_red".
The total final momentum of the system is given by:
p_final = m * v_blue + m * V_red
= m * 0.2 + m * V_red
= (0.2 + V_red)m
According to the conservation of momentum, the initial momentum must be equal to the final momentum:
p_initial = p_final
2m = (0.2 + V_red)m
Now we can solve for V_red.
Divide both sides of the equation by "m":
2 = 0.2 + V_red
Subtract 0.2 from both sides:
2 - 0.2 = V_red
1.8 = V_red
Therefore, the velocity of the red ball after the collision is 1.8 m/s.