A bus and a car have an inelastic head-on collision. The bus has a mass of 1.5 × 103 kilograms and an initial velocity of +20 meters/second. The car has a mass of 9.5 × 102 kilograms and an initial velocity of -26 meters/second. What is their total momentum after the collision?
m1v1 + m2v2
Momentum is conserved
To find the total momentum of the bus and the car after the collision, we need to use the law of conservation of momentum. According to this law, 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. In this case, the initial velocities of the bus and the car are given as +20 m/s and -26 m/s, respectively. The positive sign indicates a direction towards the right, and the negative sign indicates a direction towards the left.
Now, let's calculate the momentum of the bus and the car before the collision:
Momentum of the bus = mass of the bus × velocity of the bus
= (1.5 × 10^3 kg) × (+20 m/s) (since the bus is moving towards the right)
= 3.0 × 10^4 kg·m/s
Momentum of the car = mass of the car × velocity of the car
= (9.5 × 10^2 kg) × (-26 m/s) (since the car is moving towards the left)
= -2.47 × 10^4 kg·m/s
Now, let's find the total momentum after the collision. Since the collision is inelastic, the two objects stick together after the collision and move with a common final velocity.
Total momentum after the collision = momentum of the bus + momentum of the car
= (3.0 × 10^4 kg·m/s) + (-2.47 × 10^4 kg·m/s)
= 0.53 × 10^4 kg·m/s
Therefore, the total momentum of the bus and the car after the collision is 5,300 kg·m/s.