The mass of ball A is 10 kilograms and the mass of ball B is 5 kilograms. If
the initial velocity is set to 3 meters per second for each ball, what is the
final velocity of ball B if the final velocity of ball A is 2 meters per second?
Use the elastic collision equation to find the final velocity of ball B. Assume
ball A initially moves from right to left and ball B moves in the opposite
direction. Identify each mass, velocity, and unknown. Show your work,
including units, and indicate the direction of ball B in your answer.
To find the final velocity of ball B using the elastic collision equation, we can follow these steps:
Step 1: Identify the given information:
- Mass of ball A (mA) = 10 kilograms
- Mass of ball B (mB) = 5 kilograms
- Initial velocity of ball A (uA) = 3 meters per second
- Final velocity of ball A (vA) = 2 meters per second
Step 2: Identify the unknown:
- Final velocity of ball B (vB)
Step 3: Write down the formulas and equations needed:
To solve for the final velocity of ball B using the elastic collision equation, we use the formula:
(mA * uA) + (mB * uB) = (mA * vA) + (mB * vB)
Where:
- mA and mB are the masses of ball A and ball B, respectively.
- uA and uB are the initial velocities of ball A and ball B, respectively.
- vA and vB are the final velocities of ball A and ball B, respectively.
Step 4: Write down the equation and plug in the known values:
(mA * uA) + (mB * uB) = (mA * vA) + (mB * vB)
(10 kg * 3 m/s) + (5 kg * uB) = (10 kg * 2 m/s) + (5 kg * vB)
Step 5: Solve for the unknown:
30 kg*m/s + 5uB = 20 kg*m/s + 5vB
Step 6: Rearrange the equation to solve for vB:
5uB - 5vB = 20 kg*m/s - 30 kg*m/s
5(uB - vB) = -10 kg*m/s
(uB - vB) = -2 kg*m/s
Step 7: Solve for vB:
vB = uB + 2 kg*m/s
Based on the equation derived, the final velocity of ball B (vB) is equal to the initial velocity of ball B (uB) plus 2 kg*m/s.
Therefore, the final velocity of ball B cannot be determined unless we know the initial velocity of ball B (uB).