The mass of ball A is 10kg and the mass of ball B is 5kg. If the initial velocity is set to 3 meters per sec 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 the right to left and ball B moves the opposite direction . Identify each mass, velocity, and unknown. Show your work inckuding units, and indicate the direction of ball B in your answer.

Question

The mass of ball A is 10kg and the mass of ball B is 5kg. If the initial velocity is set to 3 meters per sec 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 the right to left and ball B moves the opposite direction . Identify each mass, velocity, and unknown. Show your work inckuding units, and indicate the direction of ball B in your answer.

Answer 1

see your 2:20PM post.

Answer 2

To find the final velocity of ball B using the elastic collision equation, we can follow these steps:

Step 1: Write down the given information:
- Mass of ball A (mA) = 10 kg
- Mass of ball B (mB) = 5 kg
- Initial velocity of ball A (uA) = 3 m/s (moving from right to left)
- Final velocity of ball A (vA) = 2 m/s (moving from right to left)

Step 2: Identify the unknown:
- Final velocity of ball B (vB) is the unknown that we need to find.

Step 3: Apply the elastic collision equation:
According to the elastic collision equation, we have:
mA * uA + mB * uB = mA * vA + mB * vB

Since we know the values for mA, uA, vA, and mB, we can plug them into the equation and solve for vB.

Step 4: Substitute the given values into the equation:
10 kg * 3 m/s + 5 kg * uB = 10 kg * 2 m/s + 5 kg * vB

Step 5: Simplify and rearrange the equation:
30 kg*m/s + 5 kg*uB = 20 kg*m/s + 5 kg*vB

Step 6: Subtract 30 kg*m/s from both sides to isolate the terms with velocities:
5 kg*uB = 20 kg*m/s + 5 kg*vB - 30 kg*m/s

Step 7: Simplify further:
5 kg*uB = -10 kg*m/s + 5 kg*vB

Step 8: Rearrange the equation to isolate vB:
5 kg*vB - 5 kg*uB = -10 kg*m/s

Step 9: Factor out the common term on the left side:
5 kg * (vB - uB) = -10 kg*m/s

Step 10: Divide both sides by 5 kg:
vB - uB = -2 m/s

Step 11: Add uB to both sides to solve for vB:
vB = -2 m/s + uB

Step 12: Substitute the value of uB (opposite direction to uA) as -3 m/s (magnitude remains the same):
vB = -2 m/s + (-3 m/s)

Step 13: Simplify:
vB = -2 m/s - 3 m/s

Step 14: Calculate the final answer:
vB = -5 m/s

Therefore, the final velocity of ball B is -5 m/s (moving from left to right).