Your bumper car is travelling at 2 m/s. The total mass of you and your car is 350 kg. An empty motionless bumper car with a mass of 250 kg is in your path. How fast in m/s will your car move after you collide with it head on?

To find the final velocity of your bumper car after colliding with the motionless car, we can use the principle of conservation of momentum.

The formula for momentum is given by:

p = m * v

Where p is the momentum, m is the mass, and v is the velocity.

Before the collision, the momentum of your car can be calculated as:

p1 = (mass1 + mass2) * velocity1

Substituting the given values:

p1 = (350 kg + 250 kg) * 2 m/s
p1 = 600 kg * 2 m/s
p1 = 1200 kg*m/s

Since the motionless car is not moving, its initial momentum (p2) is zero.

The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.

p1 + p2 = p3 + p4

Where p3 is the momentum of your car after the collision and p4 is the momentum of the motionless car after the collision.

Since the motionless car doesn't move, its final momentum (p4) is also zero.

p1 + p2 = p3 + 0

p3 = p1 + p2
p3 = 1200 kg*m/s

Now, we can find the final velocity (v3) of your car after the collision by rearranging the momentum equation:

p3 = m3 * v3

Where m3 is the mass of your car after the collision.

Solving for v3:

v3 = p3 / m3

Given that the mass of your car after the collision is 350 kg:

v3 = 1200 kg*m/s / 350 kg
v3 ≈ 3.43 m/s

Therefore, your car will move at a speed of approximately 3.43 m/s after colliding with the motionless car head-on.