A sedan weighing 4000 pounds travelling at 30mph collides head on with a compact car weighing 2000 pounds and travelling in the opposite direction at 45 mph. What is the resultant velocity of the combined vehicles?
Assume that the two cars stick together and appply that law of conservation of momentum.
4000*30 -2000*45 = 6000*Vfinal
Vfinal = (1.2*10^5 - 0.9*10^5)/6000
= 5.0 mph (in the original drection of the 4000 lb car).
I did not have to convert mass to slugs or velocities to ft/sec, because I used the same units for each term (lbmass*miles/h)
To find the resultant velocity of the combined vehicles 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.
The momentum of an object is calculated by multiplying its mass by its velocity. Let's calculate the momentum of each vehicle before the collision:
Momentum of the sedan = mass of the sedan * velocity of the sedan
= 4000 pounds * 30 mph
= 120,000 pound-mph
Momentum of the compact car = mass of the compact car * velocity of the compact car
= 2000 pounds * 45 mph
= 90,000 pound-mph
Now, let's calculate the total momentum before the collision:
Total momentum before collision = momentum of the sedan + momentum of the compact car
= 120,000 pound-mph + 90,000 pound-mph
= 210,000 pound-mph
Since momentum is conserved, the total momentum after the collision will also be 210,000 pound-mph. To find the resultant velocity, we need to rearrange the equation:
Total momentum after collision = total mass after collision * resultant velocity
To find the total mass after the collision, we add the masses of the two vehicles:
Total mass after collision = mass of the sedan + mass of the compact car
= 4000 pounds + 2000 pounds
= 6000 pounds
Now, we can plug in the values into the equation to find the resultant velocity:
Total momentum after collision = total mass after collision * resultant velocity
= 210,000 pound-mph
= 6000 pounds * resultant velocity
Dividing both sides by 6000 pounds:
Resultant velocity = 210,000 pound-mph / 6000 pounds
≈ 35 mph
Therefore, the resultant velocity of the combined vehicles after the collision is approximately 35 mph.