A 1200 kg car traveling north at 14 m/s is rear ended by a 2000 kg truck traveling at 25 m/s. If the truck and car lock bumpers and stick together, what is their speed immediately after the collision?
To find the speed of the car and the truck immediately after the collision, we can 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 (p) of an object is defined as the product of its mass (m) and its velocity (v). Mathematically, momentum can be represented as:
p = m * v
Before the collision, the momentum of the car is given by:
momentum of car (m_car * v_car) = 1200 kg * 14 m/s = 16800 kg·m/s
Similarly, the momentum of the truck before the collision is given by:
momentum of truck (m_truck * v_truck) = 2000 kg * 25 m/s = 50000 kg·m/s
Since the car and the truck stick together and move as one unit after the collision, their combined mass is the sum of their individual masses:
total mass after collision = mass of car + mass of truck = 1200 kg + 2000 kg = 3200 kg
Using the law of conservation of momentum, we can equate the total momentum before the collision to the total momentum after the collision:
Total momentum before collision = Total momentum after collision
(m_car * v_car) + (m_truck * v_truck) = total mass after collision * final velocity
Substituting the known values into the equation, we have:
(1200 kg * 14 m/s) + (2000 kg * 25 m/s) = 3200 kg * final velocity
Solving for the final velocity:
16800 kg·m/s + 50000 kg·m/s = 3200 kg * final velocity
66800 kg·m/s = 3200 kg * final velocity
final velocity = 66800 kg·m/s / 3200 kg
final velocity ≈ 20.875 m/s
Therefore, immediately after the collision, the combined car and truck will have a speed of approximately 20.875 m/s.
To determine the speed of the car and truck immediately after the collision, 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.
The formula for momentum is given by:
Momentum = mass × velocity
First, let's calculate the momentum of the car and truck before the collision. We can use the formula mentioned above.
Momentum of the car before the collision = 1200 kg × 14 m/s = 16800 kg·m/s
Momentum of the truck before the collision = 2000 kg × 25 m/s = 50000 kg·m/s
The total momentum before the collision is given by the sum of the momenta of the car and the truck:
Total momentum before collision = 16800 kg·m/s + 50000 kg·m/s = 66800 kg·m/s
Since the car and truck lock bumpers and stick together after the collision, they will move as a single unit with the same velocity.
Let's assume the final velocity of the combined car and truck is v.
Total momentum after collision = (mass of the car + mass of the truck) × v
The mass of the combined car and truck is 1200 kg + 2000 kg = 3200 kg.
According to the principle of conservation of momentum:
Total momentum before collision = Total momentum after collision
66800 kg·m/s = 3200 kg × v
Now we can solve for v:
v = 66800 kg·m/s / 3200 kg ≈ 20.875 m/s
Therefore, the combined car and truck will have a speed of approximately 20.875 m/s immediately after the collision.
momentum is conserved
(1200 * 14) + (2000 * 25) =
... (1200 + 2000) * v