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Answer :
Final answer:
The pink bumper car is moving to the right at a speed of 10 m/s.
Explanation:
To find the final velocity of the pink bumper car after the collision, we can use the principles of conservation of momentum.
Before the collision, the total momentum of the system is the sum of the momenta of both bumper cars. The momentum (p) of an object is calculated as the product of its mass (m) and velocity (v), so the initial total momentum is:
Total initial momentum = (mass of yellow car * velocity of yellow car) + (mass of pink car * velocity of pink car)
Total initial momentum = (211 kg * 8 m/s) + (151 kg * (-7 m/s))
Now, we have the total initial momentum, and after the collision, the total final momentum is the sum of the momenta of both cars. Let the final velocity of the pink car be v_final:
Total final momentum = (mass of yellow car * velocity of yellow car) + (mass of pink car * v_final)
Total final momentum = (211 kg * 7 m/s) + (151 kg * v_final)
According to the law of conservation of momentum, the total initial momentum is equal to the total final momentum:
Total initial momentum = Total final momentum
(211 kg * 8 m/s) + (151 kg * (-7 m/s)) = (211 kg * 7 m/s) + (151 kg * v_final)
Now, we can solve for v_final:
v_final = ((211 kg * 8 m/s) + (151 kg * (-7 m/s)) - (211 kg * 7 m/s)) / 151 kg
v_final ≈ 10 m/s to the right.
The negative sign indicates the direction of motion, so we use the positive sign to show the pink bumper car is moving to the right at a speed of 10 m/s.
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