Your teenage kid finally gets his drivers license. He takes off in your brand new car that weighs 2000kg at 47m/s when he hits a parked semi that weighs 40000kg. They plow forward in a perfectly in elastic fashion in the same direction. What is the velocity of the wreck?
To find the velocity of the wreck after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Initially, the momentum of the car can be calculated using the formula:
Momentum (p1) = mass × velocity
The mass of the car is 2000 kg, and the initial velocity is 47 m/s. Therefore, the momentum of the car before the collision is:
p1 = 2000 kg × 47 m/s
Similarly, the momentum of the parked semi is:
p2 = 40000 kg × 0 m/s (since the semi is stationary)
Since momentum is conserved, the sum of the initial momenta must equal the sum of the final momenta. Therefore, the momentum after the collision will be the sum of the initial momenta:
p_total = p1 + p2
Now, since the collision is perfectly inelastic, the two objects stick together and move with the same velocity. Let's call this final velocity v. So, the total momentum after the collision is:
p_total = (mass of wreck) × v
We know that the mass of the wreck is the combined mass of the car and the semi, which is:
2000 kg + 40000 kg = 42000 kg
Setting up the equation for conservation of momentum:
p1 + p2 = p_total
2000 kg × 47 m/s + 40000 kg × 0 m/s = 42000 kg × v
Now, we can solve for v:
94000 kg·m/s = 42000 kg × v
v = 94000 kg·m/s / 42000 kg
v ≈ 2.24 m/s
Therefore, the velocity of the wreck after the collision is approximately 2.24 m/s.