On a frictionless surface your bumper car is travelling at 2m/s . The total mass of you and your car is 350kg. An empty motionless bumper car with a mass of 250kg is in your path. How fast will your car move in m/s.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision:
The momentum of your car and yourself, mv1 (where m is the mass and v1 is the velocity), is given by mv1 = (350 kg)(2 m/s) = 700 kg·m/s.
The momentum of the motionless bumper car, mv2, is given by mv2 = (250 kg)(0 m/s) = 0 kg·m/s.
After the collision:
The momentum of your car and yourself is now given by (350 kg + 250 kg)v3, where v3 is the final velocity.
Using the conservation of momentum, we can equate the initial momentum to the final momentum:
mv1 + mv2 = (350 kg + 250 kg)v3
Substituting the known values, we have:
700 kg·m/s + 0 kg·m/s = (350 kg + 250 kg)v3
Simplifying the equation:
700 kg·m/s = 600 kg·v3
Dividing both sides by 600 kg:
v3 = 700 kg·m/s / 600 kg = 1.17 m/s
Therefore, your car will move at a speed of 1.17 m/s after the collision.