momentum is conserved
10 kg * 5 m/s = (10 kg * 1 m/s) + (2 kg * v m/s)
solve for v
10 kg * 5 m/s = (10 kg * 1 m/s) + (2 kg * v m/s)
solve for v
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.