How to calculate distance object traveled in completely inelastic collision?

[pebbles]

Ok, so I have this practice problem: a mass of 5 kg has hit a ball at 8 m/s. The ball it hit has a mass of 7 kg. What is the distance the ball traveled?


It's really frustrating when my notes don't go over ANY of this.

 

[Galileo]

Are you sure that's the entire problem statement? It doesn't make much sense as it is.
Distance traveled as in: how far from the moment of impact till it hits the ground? That would depend on the height at which the collision took place.

 

[ogb p]

To calculate the distance traveled in a completely inelastic collision, we can use the conservation of momentum equation, which states that the total momentum before the collision is equal to the total momentum after the collision. In this case, the momentum before the collision is calculated by multiplying the mass of the object (5 kg) by its initial velocity (8 m/s), giving us a total momentum of 40 kg*m/s. After the collision, the two objects stick together and move with the same final velocity.

To find the final velocity, we can use the conservation of kinetic energy equation, which states that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. In this case, the kinetic energy before the collision is calculated by using the mass of the two objects (5 kg + 7 kg = 12 kg) and the initial velocity (8 m/s), giving us a total kinetic energy of 384 J. After the collision, the kinetic energy is converted into potential energy due to the objects sticking together, so we can use the equation PE = mgh to find the height (h) that the objects reached. Since the objects are now at rest, the final velocity is 0 m/s, so we can substitute that into the equation to get PE = 12 kg * 9.8 m/s^2 * h = 0. Solving for h, we get h = 0 m.

Now that we have the final velocity (0 m/s) and the initial velocity (8 m/s), we can use the equation for average velocity (v = (vi + vf)/2) to find the distance traveled. Plugging in the values, we get v = (8 m/s + 0 m/s)/2 = 4 m/s. We can then use the equation for distance (d = vt) to find the distance traveled, where v is the average velocity and t is the time. Since we don't have the time, we can use the fact that the objects are at rest to determine that the time is equal to the distance traveled divided by the final velocity, giving us t = d/0 m/s = undefined. This means that the distance traveled by the ball is infinite, as it continues to travel with the mass of 12 kg at a velocity of 4 m/s.

In summary, the distance traveled by the ball in this completely inelastic collision is infinite. It is important to note that