A 12000 kg truck strikes the back end of a 750 kg car moving at 15 m/s. If the truck loses 7500 kg-m/s of its momentum to the car, what is the car's velocity after the collision?
I'm not sure how to solve this one... Help please?!
To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Step 1: Calculate the initial momentum of the truck and car:
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v): p = m * v.
Initial momentum of the truck = mass of truck * velocity of truck = 12,000 kg * 0 m/s (since the truck is initially stationary) = 0 kg-m/s.
Initial momentum of the car = mass of car * velocity of car = 750 kg * 15 m/s = 11,250 kg-m/s.
Step 2: Calculate the final momentum of the truck and car.
The truck loses 7,500 kg-m/s of its momentum to the car during the collision. Therefore, the final momentum of the truck after the collision (Pft) is calculated by subtracting the amount of momentum transferred to the car (7500 kg-m/s) from the initial momentum of the truck (0 kg-m/s): Pft = 0 kg-m/s - 7500 kg-m/s = -7500 kg-m/s.
The final momentum of the car after the collision (Pfc) can be obtained by adding the amount of momentum transferred from the truck (7500 kg-m/s) to the initial momentum of the car (11,250 kg-m/s): Pfc = 11,250 kg-m/s + 7500 kg-m/s = 18,750 kg-m/s.
Step 3: Calculate the final velocity of the car.
The final velocity (vf) of an object can be calculated by dividing its final momentum (Pf) by its mass (m): vf = Pf / m.
Final velocity of the car = final momentum of the car / mass of the car = 18,750 kg-m/s / 750 kg = 25 m/s.
Therefore, the car's velocity after the collision is 25 m/s.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, 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. Therefore, the momentum of the truck before the collision is given by:
Momentum of truck before collision = (mass of truck) x (velocity of truck)
Similarly, the momentum of the car before the collision is given by:
Momentum of car before collision = (mass of car) x (velocity of car)
After the collision, the truck loses 7500 kg-m/s of its momentum to the car. Therefore, the momentum of the truck after the collision is:
Momentum of truck after collision = (mass of truck) x (velocity of truck after collision)
The momentum of the car after the collision is given by:
Momentum of car after collision = (mass of car) x (velocity of car after collision)
According to the conservation of momentum:
(Momentum of truck before collision) + (Momentum of car before collision) = (Momentum of truck after collision) + (Momentum of car after collision)
Using the given values, we can substitute them into the equation and solve for the velocity of the car after the collision.
momentum is conserved, so the truck's loss is the car's gain
7500 kg-m/s / 750 kg = ?