A 1180 kg car and 4720 kg truck undergo a perfectly inelastic collision. Before the collision, the car was traveling southward at 1.45 m/s , and the truck westward at 8.80 m/s.
Find the velocity of the wreckage immediately after the collision.
Enter the x and y components of the velocity separated by a comma. Assume that the positive x and y axes are directed eastward and northward, respectively.
momentum is conserved
x-component
... -8.80 [4720 / (4720 + 1180)]
y-component
... -1.45 [1180 / (1180 + 4720)]
v = √(x^2 + y^2)
the tangent of the reference angle in quad III is ... y/x
To find the velocity of the wreckage immediately after the collision, we can use the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity.
Before the collision, the momentum of the car can be calculated as:
Momentum of the car = mass of the car * velocity of the car
= 1180 kg * 1.45 m/s
= 1711 kg m/s (southward)
Before the collision, the momentum of the truck can be calculated as:
Momentum of the truck = mass of the truck * velocity of the truck
= 4720 kg * (-8.80 m/s)
= -41536 kg m/s (westward)
In the collision, the car and truck stick together and move as one unit.
To calculate the velocity of the wreckage after the collision, we can use the principle of conservation of momentum:
Total momentum before collision = Total momentum after collision
Therefore,
(1711 kg m/s (southward)) + (-41536 kg m/s (westward)) = (Total mass of car and truck) * (velocity of the wreckage)
The total mass of the car and truck = mass of the car + mass of the truck
= 1180 kg + 4720 kg
= 5900 kg
Now, let's calculate the x and y components of the velocity of the wreckage.
The x component of the velocity of the wreckage = (Total momentum before collision in x direction) / (Total mass of car and truck)
Total momentum before collision in x direction = momentum of the truck
= -41536 kg m/s (westward)
The y component of the velocity of the wreckage = (Total momentum before collision in y direction) / (Total mass of car and truck)
Total momentum before collision in y direction = momentum of the car
= 1711 kg m/s (southward)
Therefore,
x component of velocity of the wreckage = -41536 kg m/s / 5900 kg
= -7.045 m/s (westward)
y component of velocity of the wreckage = 1711 kg m/s / 5900 kg
= 0.290 m/s (southward)
So, the velocity of the wreckage immediately after the collision is:
x component = -7.045 m/s (westward)
y component = 0.290 m/s (southward)
Therefore, the velocity of the wreckage immediately after the collision is (-7.045 m/s, 0.290 m/s).
To find the velocity of the wreckage immediately after the collision, 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 given by the product of its mass and velocity. In this case, we need to find the total momentum in the x and y directions separately.
Let's assume that the positive x-axis points eastward and the positive y-axis points northward.
Before the collision, the momentum of the car in the x-direction is given by:
Momentum_car_x = (mass_car) * (velocity_car_x)
= (1180 kg) * (0 m/s), since the car is traveling southward
Before the collision, the momentum of the car in the y-direction is given by:
Momentum_car_y = (mass_car) * (velocity_car_y)
= (1180 kg) * (0 m/s), since the car is traveling southward
Before the collision, the momentum of the truck in the x-direction is given by:
Momentum_truck_x = (mass_truck) * (velocity_truck_x)
= (4720 kg) * (-8.8 m/s), since the truck is traveling westward
Before the collision, the momentum of the truck in the y-direction is given by:
Momentum_truck_y = (mass_truck) * (velocity_truck_y)
= (4720 kg) * (0 m/s), since the truck is traveling westward
The total momentum before the collision in the x-direction is the sum of the momenta of the car and the truck:
Total_momentum_x = Momentum_car_x + Momentum_truck_x
The total momentum before the collision in the y-direction is the sum of the momenta of the car and the truck:
Total_momentum_y = Momentum_car_y + Momentum_truck_y
Now, we know the total momentum before the collision. According to the principle of conservation of momentum, the total momentum after the collision is also equal to the total momentum before the collision.
Since the collision is perfectly inelastic, the wreckage moves together with a common final velocity.
Therefore, the velocity of the wreckage immediately after the collision in the x-direction is the sum of the momenta of the car and the truck divided by the total mass of the system:
Velocity_wreckage_x = (Total_momentum_x) / (Total_mass)
Similarly, the velocity of the wreckage immediately after the collision in the y-direction is the sum of the momenta of the car and the truck divided by the total mass of the system:
Velocity_wreckage_y = (Total_momentum_y) / (Total_mass)
Now, we can calculate the velocity of the wreckage immediately after the collision by substituting the given values into the above equations.