Question
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
.
Bumper car
If the cars have an elastic collision,
what would the velocity of car 2 be
afterwards?
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:
-
Calculate the Numerator:
-
Calculate the Denominator:
-
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.