Car A, with a mass of 1250 kg, is traveling at 30 m/s to the east. A truck with mass of 2000 kg, traveling to the west at 25 m/s. An inelastic collision occurred, not sticking together, the car goes off 10 m/s to the west. What is the resulting velocity of the truck?
McVv+MtVt must remain unchanged before and after the collision, so
(1250)(30)+(2000)(-25) = 1250(-10)+2000v
v=0
so, the truck comes to a stop and knocks the car backwards.
To find the resulting velocity of the truck after the collision, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the initial velocities of the car and the truck as v1 and v2, respectively. The initial momentum of the car is given by (mass of car * velocity of car), and the initial momentum of the truck is given by (mass of truck * velocity of truck).
Initial momentum of the car = (mass of car) * (velocity of car) = (1250 kg) * (30 m/s) = 37500 kg * m/s
Initial momentum of the truck = (mass of truck) * (velocity of truck) = (2000 kg) * (-25 m/s) = -50000 kg * m/s (since the truck is traveling west, we take the velocity as negative)
Let the final velocity of the truck be vf. Since the car goes off at 10 m/s to the west, we take the velocity of the car after the collision as -10 m/s.
Final momentum of the car = (mass of car) * (velocity of car after collision) = (1250 kg) * (-10 m/s) = -12500 kg * m/s
According to the principle of conservation of linear momentum, the total initial momentum = total final momentum.
Total initial momentum = Initial momentum of the car + Initial momentum of the truck = 37500 kg * m/s + (-50000 kg * m/s) = -12500 kg * m/s
Total final momentum = Final momentum of the car + Final momentum of the truck = -12500 kg * m/s + (mass of truck) * (vf)
Setting the initial momentum equal to the final momentum, we have:
-12500 kg * m/s = -12500 kg * m/s + (2000 kg) * (vf)
Simplifying the equation:
0 = (2000 kg) * (vf)
Dividing both sides of the equation by 2000 kg:
0 = vf
Therefore, the resulting velocity of the truck after the collision is 0 m/s.