Two 125 kg bumper cars are moving toward each other in opposite directions. Car X is moving at 10 m/s and Car Z at –12 m/s when they collide head–on. If the resulting velocity of Car Z after the collision is 10 m/s, what is the velocity of Car X after the collision?
It would be nice to know the direction of Car Z. And it would be nice to know if it were an elastic collision, in reality, it is not.
-12
To solve this problem, we can use the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision. Momentum is calculated by multiplying mass and velocity.
Let's assume the velocity of Car X after the collision is v1.
The momentum before the collision can be calculated as:
Momentum of car X before collision = Mass of car X * Velocity of car X
Momentum of car X before collision = 125 kg * 10 m/s = 1250 kg·m/s
The momentum before the collision for Car Z can be calculated as:
Momentum of car Z before collision = Mass of car Z * Velocity of car Z
Momentum of car Z before collision = 125 kg * (-12 m/s) = -1500 kg·m/s (since the velocity is in the opposite direction, we include a negative sign)
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
Total momentum before collision = Total momentum after collision
Total momentum before collision = Momentum of car X before collision + Momentum of car Z before collision
Total momentum before collision = 1250 kg·m/s + (-1500 kg·m/s) = -250 kg·m/s
Now, we can calculate the momentum after the collision for Car Z using the given information:
Momentum of car Z after collision = Mass of car Z * Velocity of car Z after collision
Momentum of car Z after collision = 125 kg * 10 m/s = 1250 kg·m/s
Finally, we can find the velocity of Car X after the collision using the law of conservation of momentum:
Total momentum after collision = Momentum of car X after collision + Momentum of car Z after collision
Total momentum after collision = Momentum of car X after collision + Momentum of car Z after collision
-250 kg·m/s = Mass of car X * Velocity of car X after collision + 1250 kg·m/s
Rearranging the equation, we can solve for the velocity of Car X after the collision:
Mass of car X * Velocity of car X after collision = -250 kg·m/s - 1250 kg·m/s
Mass of car X * Velocity of car X after collision = -1500 kg·m/s
Velocity of car X after collision = -1500 kg·m/s / Mass of car X
Substituting the given mass of Car X, which is 125 kg, we can calculate the velocity of Car X after the collision:
Velocity of car X after collision = -1500 kg·m/s / 125 kg
Velocity of car X after collision = -12 m/s
Therefore, the velocity of Car X after the collision is -12 m/s. The negative sign indicates that the car is moving in the opposite direction as previously indicated.