bounce collision

Question

A 2000-kg car going 30 m/s collides head-on with a 5000-kg truck going at the same speed. If the truck comes to a halt, The car's final velocity is 

Answer 1

The final velocity of the car can be determined using the principle of conservation of momentum. This principle states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision.

In this case, the system consists of the car and the truck, and the collision is head-on. The initial momentum of the car is p1 = m1v1 = (2000 kg)(30 m/s) = 60000 kgm/s. The initial momentum of the truck is p2 = m2v2 = (5000 kg)(30 m/s) = 150000 kgm/s.

After the collision, the truck comes to a halt, so its final velocity is v2f = 0 m/s. The final momentum of the truck is p2f = m2v2f = (5000 kg)(0 m/s) = 0 kg*m/s.

The principle of conservation of momentum states that the initial momentum of the system is equal to the final momentum of the system, so we can write the equation:

p1 + p2 = p1f + p2f

Substituting in the known values, we get:

60000 kgm/s + 150000 kgm/s = p1f + 0 kg*m/s

Solving for p1f, we get:

p1f = p1 + p2 - p2f = 60000 kgm/s + 150000 kgm/s - 0 kgm/s = 210000 kgm/s

To find the final velocity of the car, we can divide the final momentum by the mass of the car:

v1f = p1f/m1 = 210000 kg*m/s / 2000 kg = 105 m/s

So the final velocity of the car is 105 m/s.