A 2050 kg truck is traveling east through an intersection at 2.3 m/s when it is hit simultaneously from the side and the rear. (Some people have all the luck!) One car is a 1200 kg compact traveling north at 4.5 m/s. The other is a 1600 kg midsize traveling east at 10 m/s. The three vehicles become entangled and slide as one body. What are their speed and direction just after the collision?
To find the speed and direction of the vehicles just after the collision, we can apply 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.
Let's assign positive directions as follows:
- Eastward direction is positive for the truck and the midsize car.
- Northward direction is positive for the compact car.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
The total momentum before the collision can be calculated as follows:
Total momentum before = (mass of truck * velocity of truck) + (mass of compact car * velocity of compact car) + (mass of midsize car * velocity of midsize car)
= (2050 kg * 2.3 m/s) + (1200 kg * 4.5 m/s) + (1600 kg * 10 m/s)
To find the speed and direction of the vehicles just after the collision, we first need to find the total momentum after the collision. Since the vehicles become entangled and slide as one body, the total mass after the collision is the sum of the masses of the truck, compact car, and midsize car.
Total mass after = mass of truck + mass of compact car + mass of midsize car
Next, we divide the total momentum after the collision by the total mass after the collision to find the velocity:
Velocity after = Total momentum after / Total mass after
Finally, we can determine the speed and direction of the vehicles just after the collision by determining the magnitude and direction of the velocity vector.
Let's calculate the values step-by-step:
1. Calculate the total momentum before the collision:
Total momentum before = (2050 kg * 2.3 m/s) + (1200 kg * 4.5 m/s) + (1600 kg * 10 m/s)
2. Calculate the total mass after the collision:
Total mass after = 2050 kg + 1200 kg + 1600 kg
3. Calculate the velocity after the collision:
Velocity after = Total momentum before / Total mass after
4. Determine the magnitude and direction of the velocity vector to find the speed and direction after the collision.
Please provide the values for the mass of the truck, the velocity of the truck, the velocity of the compact car, and the velocity of the midsize car so that I can calculate the speed and direction after the collision.
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the collision should be equal to the total momentum after the collision.
Let's start by calculating the initial momentum of each vehicle:
Initial momentum of the truck = mass of truck * velocity of truck
= 2050 kg * 2.3 m/s
Initial momentum of the compact car = mass of compact car * velocity of compact car
= 1200 kg * 4.5 m/s
Initial momentum of the midsize car = mass of midsize car * velocity of midsize car
= 1600 kg * 10 m/s
Now, let's consider the final momentum. Since the three vehicles become entangled and slide as one body, their total mass will be the sum of their individual masses.
Total mass after collision = mass of truck + mass of compact car + mass of midsize car
Total momentum after collision = Total mass after collision * final velocity
Since we want to find the final velocity, we can write the equation as:
Total mass after collision * final velocity = initial momentum of the truck + initial momentum of the compact car + initial momentum of the midsize car
Now, we can plug in the given values and solve for the final velocity:
Total mass after collision = 2050 kg + 1200 kg + 1600 kg
= 4850 kg
Initial momentum of the truck = 2050 kg * 2.3 m/s
= 4715 kg·m/s
Initial momentum of the compact car = 1200 kg * 4.5 m/s
= 5400 kg·m/s
Initial momentum of the midsize car = 1600 kg * 10 m/s
= 16000 kg·m/s
4850 kg * final velocity = 4715 kg·m/s + 5400 kg·m/s + 16000 kg·m/s
Now, we can solve for final velocity:
final velocity = (4715 kg·m/s + 5400 kg·m/s + 16000 kg·m/s) / 4850 kg
After performing the calculation, you will find the final velocity. The direction of the final velocity can be determined by considering the direction of motion of the vehicles before the collision.