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Answer :
Final answer:
In an elastic collision between bumper cars, the final speeds can be calculated using the conservation of momentum. By setting up the equation and rearranging it, we can find the final velocity of the trailing bumper car. The correct answer is option c) 6.00 m/s, 5.60 m/s.
Explanation:
In an elastic collision, the final speeds of the bumper cars can be determined using the conservation of momentum. Since the mass of the leading bumper car is 30.0% greater than that of the trailing bumper car, we can calculate the new masses as follows:
Mass of trailing bumper car = m
Mass of leading bumper car = m + 30% of m = m + 0.3m = 1.3m
Using the conservation of momentum, we can set up the equation:
(Mass of trailing bumper car) x (Initial velocity of trailing bumper car) + (Mass of leading bumper car) x (Initial velocity of leading bumper car) = (Mass of trailing bumper car) x (Final velocity of trailing bumper car) + (Mass of leading bumper car) x (Final velocity of leading bumper car)
Plugging in the given values:
(m) x (5.60 m/s) + (1.3m) x (6.00 m/s) = (m) x (Final velocity of trailing bumper car) + (1.3m) x (Final velocity of leading bumper car)
Simplifying the equation:
5.60m + 7.8m = Final velocity of trailing bumper car + 1.3(Final velocity of leading bumper car)
Combining like terms:
13.4m = Final velocity of trailing bumper car + 1.3(Final velocity of leading bumper car)
We can rearrange the equation to solve for the final velocity of the trailing bumper car:
Final velocity of trailing bumper car = 13.4m - 1.3(Final velocity of leading bumper car)
Since the mass and initial velocity of the cars are given, we can substitute the values:
(Final velocity of leading bumper car) = 6.00 m/s
(m) = mass of the trailing bumper car
Final velocity of trailing bumper car = 13.4m - 1.3(6.00 m/s)
Final velocity of trailing bumper car = 13.4m - 7.8 m/s = 5.6 m/s
Therefore, the correct answer is option c) 6.00 m/s, 5.60 m/s.
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