A 10 kg ball moving at 5 m/s collides elastically with a stationary 2 kg ball. After the collision , the 10 kg ball is moving at 1 m/s in the same direction. What is the velocity of the 2 kg ball?
momentum is conserved
10 kg * 5 m/s = (10 kg * 1 m/s) + (2 kg * v m/s)
solve for v
To find the velocity of the 2 kg 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 of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) is given by the equation:
p = m * v
where p is momentum, m is mass, and v is velocity.
Before the collision, the 10 kg ball is moving at 5 m/s, and the 2 kg ball is stationary. Therefore, the initial momentum of the system is:
initial momentum = (mass of 10 kg ball * velocity of 10 kg ball) + (mass of 2 kg ball * velocity of 2 kg ball)
= (10 kg * 5 m/s) + (2 kg * 0 m/s)
= 50 kg*m/s
After the collision, the 10 kg ball is moving at 1 m/s in the same direction. We need to find the velocity of the 2 kg ball, which we'll denote as v2.
The momentum after the collision becomes:
momentum after collision = (mass of 10 kg ball * velocity of 10 kg ball) + (mass of 2 kg ball * velocity of 2 kg ball)
= (10 kg * 1 m/s) + (2 kg * v2)
Since the collision is elastic, the total momentum before the collision is equal to the total momentum after the collision. Therefore:
initial momentum = momentum after collision
50 kg*m/s = (10 kg * 1 m/s) + (2 kg * v2)
Simplifying the equation, we have:
50 kg*m/s = 10 kg*m/s + 2 kg * v2
Rearranging the equation to solve for v2:
2 kg * v2 = 50 kg*m/s - 10 kg*m/s
2 kg * v2 = 40 kg*m/s
v2 = 40 kg*m/s / 2 kg
v2 = 20 m/s
Therefore, the velocity of the 2 kg ball after the collision is 20 m/s in the same direction.