Final answer:
By using the conservation of momentum, the speed and direction after the collision can be calculated. The total momentum before collision is -10150 kg·m/s, and after the collision, the cars move together with a speed of 12.08 m/s to the left. The closest given option is 10 m/s left.
Step-by-step explanation:
To determine the speed and direction of the two cars after the collision, we can apply the principle of conservation of momentum. The total momentum before the collision is the sum of the individual momenta of the BLUE and RED cars, which can be calculated as follows:
- Momentum of BLUE car = mass × velocity = 490 kg × 35 m/s (left).
- Momentum of RED car = mass × velocity = 350 kg × 20 m/s (right).
Since the RED car is traveling to the right, its momentum is taken as positive, and the BLUE car is traveling to the left, so its momentum is taken as negative:
Total momentum before collision = (-490 kg × 35 m/s) + (350 kg × 20 m/s) = -17150 kg·m/s + 7000 kg·m/s = -10150 kg·m/s.
After the collision, the cars lock bumpers and move together, so their combined mass is 490 kg + 350 kg = 840 kg. Using conservation of momentum, the total momentum before the collision will be equal to the total momentum after the collision. The velocity (v) after the collision can be found by dividing the total momentum by the combined mass:
v = Total momentum / Combined mass = -10150 kg·m/s / 840 kg = -12.08 m/s.
Since the result is negative, the direction is to the left. The speed is the absolute value of velocity, so the speed is 12.08 m/s. None of the options exactly match, but the closest option in magnitude and the correct direction is:
c) 10 m/s left