A 0.600-kg ball traveling 4.00 m/s to the right collides with a 1.00-kg ball traveling
5.00 m/s to the left. After the collision, the lighter ball is traveling 7.25 m/s to the
left. What is the velocity of the heavier ball after the collision?
(0.600*4.00+1.00*(-5.00)-0.600*(-7.25))/1.00 = 1.75
I put parenthesis just to show the negative numbers, but the whole problem should be put in the parenthesis then divide by 1.00 in a calculator
conserve momentum:
0.600(+4.00) + 1.00(-5.00) = 1.00(-7.25) + 0.600v
v = +7.75
Now, what's wrong with this picture?
To find the velocity of the heavier 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 can be expressed as:
momentum = mass * velocity
Let's break down the information given in the problem:
Mass of the first ball (lighter ball): m1 = 0.600 kg
Initial velocity of the first ball: v1-initial = 4.00 m/s
Mass of the second ball (heavier ball): m2 = 1.00 kg
Initial velocity of the second ball: v2-initial = 5.00 m/s
After the collision, the lighter ball is traveling with a velocity of v1-final = -7.25 m/s (negative because it is moving to the left). We need to find the velocity of the heavier ball, v2-final.
Using the conservation of momentum equation, we can write:
(m1 * v1-initial) + (m2 * v2-initial) = (m1 * v1-final) + (m2 * v2-final)
Now, let's substitute the values:
(0.600 kg * 4.00 m/s) + (1.00 kg * -5.00 m/s) = (0.600 kg * -7.25 m/s) + (1.00 kg * v2-final)
Simplifying the equation:
2.4 - 5.0 = -4.35 + v2-final
-2.6 = -4.35 + v2-final
Adding 4.35 to both sides of the equation:
1.75 = v2-final
Therefore, the velocity of the heavier ball after the collision is 1.75 m/s to the left.