Question

Two identical cars are driving directly toward each other with speeds of 50 mph and 60 mph. Find their combined speed if the collision is perfectly inelastic.

Answer 1

In a perfectly inelastic collision of two identical cars approaching each other with speeds of 50 mph and 60 mph, their combined speed after the collision will be the difference between the two speeds in the travel direction of the faster car, considering momentum conservation.

Step-by-step explanation:

Calculating Combined Speed in Inelastic Collision

When two identical cars collide head-on with speeds of 50 mph and 60 mph, and the collision is perfectly inelastic, the combined speed of the cars after the collision is not simply the sum of the two speeds. An inelastic collision is one in which the two objects stick together after impact. The conservation of momentum must be taken into account because momentum is conserved in all collisions. In a perfectly inelastic collision, the two cars stick together after the collision and move as a single object. Therefore, to find the combined speed after the collision, we add the momentum (mass × velocity) of the two cars before the collision and then divide by the total mass of the combined object.

Since the cars are identical and their masses cancel out, the combined speed is the vector sum of their speeds. However, because they are moving directly toward each other, one will have a negative velocity to indicate the opposite direction. So if we take the direction of the 50 mph car as positive, the 60 mph car would have a negative velocity. The combined speed would not be a simple arithmetic sum, but a case where the magnitude of the combined momentum divided by the total mass gives us the speed (which in this case equals the velocity because they are moving in a straight line).

Mathematically, this would mean:

• Total momentum before collision = (mass × 50 mph) + (mass × (-60 mph))
• Combined speed after collision = (Total momentum) / (Total mass)

For identical masses, the speeds effectively subtract because they are in opposite directions, so the combined speed after the collision is the difference in their speeds while keeping their original travel direction.