Question
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Bumper car moves east at .
Bumper car ) moves west at .
If the cars have an elastic collision,
what would the velocity of car 2 be
afterwards?
Remember: East is positive ; west is negative .

Ask by Clark Turner. in South Africa
Jan 22,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

After the collision, Bumper Car 2 moves east at approximately 3.49 m/s.

Solution

To determine the final velocity of bumper car after an elastic collision, we’ll use the principles of conservation of momentum and kinetic energy. Here’s a step-by-step breakdown:

Given:

  • Mass of Car 1 ( ):
  • Initial Velocity of Car 1 ( ): (East, positive)
  • Mass of Car 2 ( ):
  • Initial Velocity of Car 2 ( ): (West, negative)

Formula for Final Velocity in an Elastic Collision:

The final velocity ( ) of Car 2 after an elastic collision is given by:

Plugging in the Values:

  1. Calculate the Numerator:
  2. Calculate the Denominator:
  3. Compute :

Conclusion:

After simplifying, the final velocity of Bumper Car 2 is approximately:
Answer: After the collision, car 2 moves east with velocity 3.49  m s⁻¹.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Extra Insights

To solve for the final velocity of bumper car 2 after an elastic collision, we can use the conservation of momentum and the conservation of kinetic energy principles.

Step 1: Conservation of Momentum

The formula for conservation of momentum is:
Where:
  • (mass of car 1)
  • (initial velocity of car 1)
  • (mass of car 2)
  • (initial velocity of car 2, negative because it moves west)

Step 2: Conservation of Kinetic Energy

The formula for conservation of kinetic energy is:

Step 3: Solving for Final Velocities

Using both equations together and simplifying will yield the final velocities.
After carrying out the calculations (omitting intermediary steps for brevity):
The final velocity of car 2, , is approximately to the east.

Answer:

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