a 1200kg car traveling initially qith a speeed of 25.0 m/s in an easterly direction crashes into the rear end of a 9,000kg truck moving in the same direction at 20.0 m/s. the velocity of the car right after the collision is 18.0 m/s to the east. what is the celocity of the truck right after the collision?
Since this is NOT an elastic collision, only momentum is conserved. You only need to conside momentum on east-west (x) direction.
Mcar*25.0 + Mtruck*20.0 = Mcar*18.0 + Mtruck*V
V is the velocity you want.
210,000 = 21,600 + 9000 V
V = 20.93 s
To find the velocity of the truck right after the collision, we can use the principle of conservation of momentum.
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In this case, the system consists of the car and the truck.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Before the collision, we can calculate the momentum of the car and the truck separately:
Momentum of the car before the collision:
= mass of the car × velocity of the car
= 1200 kg × 25.0 m/s
Momentum of the truck before the collision:
= mass of the truck × velocity of the truck
= 9000 kg × 20.0 m/s
Since the car crashes into the rear end of the truck, no external forces act on the system except for the internal forces between the car and the truck. Therefore, the total momentum of the system is conserved.
Total momentum before the collision = Total momentum after the collision
(1200 kg × 25.0 m/s) + (9000 kg × 20.0 m/s) = (1200 kg × 18.0 m/s) + (9000 kg × v)
Solving for v, the velocity of the truck after the collision:
(1200 kg × 25.0 m/s) + (9000 kg × 20.0 m/s) = (1200 kg × 18.0 m/s) + (9000 kg × v)
(30,000 kg·m/s) + (180,000 kg·m/s) = (21,600 kg·m/s) + (9000 kg × v)
210,000 kg·m/s = 21,600 kg·m/s + (9000 kg × v)
210,000 kg·m/s - 21,600 kg·m/s = 9000 kg × v
188,400 kg·m/s = 9000 kg × v
Dividing both sides of the equation by 9000 kg:
v = 188,400 kg·m/s / 9000 kg
v ≈ 20.933 m/s
Therefore, the velocity of the truck right after the collision is approximately 20.933 m/s to the east.