A ball A of mass 0.2kg losses one third of it's velocity when it makes a head collision with identical ball B move off with a speed 20m/s in the original direction of B.calculate the initial velocity of B
To calculate the initial velocity of ball B, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the initial velocity of ball A as vA and the initial velocity of ball B as vB. We know that ball A loses one-third of its velocity, so after the collision, it moves at a speed of vA/3. Ball B moves off with a speed of 20 m/s in the original direction of B.
The momentum before the collision can be calculated as the product of mass and velocity, and since the masses of both balls are the same, the momentum equation becomes:
(mass of A * velocity of A) + (mass of B * velocity of B) = (mass of A * final velocity of A) + (mass of B * final velocity of B)
Substituting the given values, we get:
(0.2 kg * vA) + (0.2 kg * vB) = (0.2 kg * vA/3) + (0.2 kg * 20 m/s)
Simplifying the equation:
0.2 kg * vA + 0.2 kg * vB = 0.2 kg * vA/3 + 4 kg
Multiply through by 10 to eliminate decimals:
2 kg * vA + 2 kg * vB = 2 kg * vA/3 + 40 kg
Now, let's simplify the equation further:
6 kg * vA + 6 kg * vB = 2 kg * vA + 120 kg
4 kg * vA = 6 kg * vB - 120 kg
Divide both sides by 4 kg:
vA = (6/4) * vB - 30 m/s
Therefore, the initial velocity of ball B (vB) is:
vB = (vA + 30 m/s) * 4/6
Since we do not have the precise value of vA, we cannot determine the exact initial velocity of B using this equation. However, once you know the initial velocity of ball A, you can substitute it into the equation to calculate the initial velocity of ball B.