Two cars have a head-on collision. Both were traveling at 28 m/s toward each other. Car A has a mass of 700 kg and car B has a mass of 904 kg. After the impact, what is car B's velocity?
Again,this cannot be solved without some assumption on energy, and in a head on collision, conservation of mechanical energy is out of the question. If you have other thoughts, I would like to hear them.
12 m/s
To find car B's velocity after the collision, we need to apply 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, provided there are no external forces acting on the system.
The momentum of an object is defined as the product of its mass (m) and velocity (v). Therefore, the momentum (p) can be expressed as p = mv.
Before the collision, car A and car B are traveling towards each other, so the total momentum before the collision is the sum of their individual momentum.
The momentum of car A before the collision is given by:
pA = mA * vA
The momentum of car B before the collision is given by:
pB = mB * vB
Since both cars are traveling at the same speed of 28 m/s towards each other, their velocities have opposite directions. The magnitude of the velocity is the same, but we need to consider the directional difference.
Considering car A's velocity as positive and car B's velocity as negative, the equation representing the total momentum before the collision is:
p_total = pA + pB = mA * vA + (-mB * vB)
After the collision, the cars come to a stop, meaning their total momentum becomes zero. Therefore, the equation for the total momentum after the collision is:
p_total = 0
Now, we can solve for car B's velocity (vB) using these equations. Substituting the given values, we have:
mA * vA + (-mB * vB) = 0
Rearranging the equation, we can isolate vB:
-mB * vB = -mA * vA
Dividing both sides by -mB, we get:
vB = (mA * vA) / mB
Replacing the values for mA, vA, and mB, we have:
vB = (700 kg * 28 m/s) / 904 kg
Calculating the expression on the right:
vB ≈ 21.81 m/s
Therefore, car B's velocity after the impact is approximately 21.81 m/s.