Car A with mass of 1250 kg is traveling at 30 m/s to the east. Car B is a truck with mass of 2000 kg, traveling to the west at 25 m/s. Assume these two vehicles experience an inelastic collision but do not stick together and car a goes off 10 m/s to the west. What will be the resulting velocity of car B?
I have the same problem
To solve this problem, we can apply the principles of conservation of momentum. The total momentum before the collision should equal the total momentum after the collision.
Momentum (p) is defined as the product of an object's mass (m) and velocity (v):
p = m * v
We have two vehicles involved in the collision, Car A and Car B. Before the collision, Car A has a mass of 1250 kg and is moving to the east at 30 m/s. Car B has a mass of 2000 kg and is moving to the west at 25 m/s.
To find the total momentum before the collision, we can add the momenta of Car A and Car B:
Total momentum before collision = momentum of Car A + momentum of Car B
Momentum of Car A = (mass of Car A) * (velocity of Car A)
= (1250 kg) * (30 m/s) = 37500 kg·m/s (to the east)
Momentum of Car B = (mass of Car B) * (velocity of Car B)
= (2000 kg) * (-25 m/s) = -50000 kg·m/s (to the west)
Total momentum before collision = 37500 kg·m/s + (-50000 kg·m/s)
= -12500 kg·m/s
Since momentum is conserved, the total momentum after the collision should also be -12500 kg·m/s.
Now, we can find the resulting velocity of Car B after the collision. Let's assume its velocity is v_Bf (final velocity of Car B).
Total momentum after collision = momentum of Car A after collision + momentum of Car B after collision
The momentum of Car A after the collision can be calculated using its mass and final velocity:
Momentum of Car A after collision = (mass of Car A) * (velocity of Car A after collision)
= (1250 kg) * (-10 m/s) = -12500 kg·m/s (to the west)
Understanding that the momentum after the collision should be -12500 kg·m/s, we can now find the velocity of Car B after the collision:
Total momentum after collision = -12500 kg·m/s + momentum of Car B after collision
-12500 kg·m/s = -12500 kg·m/s + momentum of Car B after collision
momentum of Car B after collision = 0 kg·m/s
The momentum of Car B after the collision is zero since it experienced an inelastic collision but did not stick together. Therefore, the final velocity of Car B is 0 m/s.