Particle Collision: Cars Collide at Intersection - Magnitude & Direction

In summary, particle collisions occur when two or more particles collide and transfer energy, causing a change in their direction and/or magnitude. Cars can collide at an intersection due to various factors, such as failure to yield or not following traffic signals. The magnitude of a car collision is determined by factors like speed, weight, and angle of impact. The direction of a car collision is influenced by the direction of travel before the collision. The consequences of a car collision can range from minor damage to serious injuries or fatalities, as well as legal and financial consequences.
  • #1
skatecash
3
0
A 1100 kg car traveling north (+j) at 70 km/h collides at an intersection with a 2000 kg car traveling west (-i) at 48 km/h. The two cars stick together.
Find the magnitude and direction of the velocity of the wreckage just after the collision

I did pythag. thereom and got 84.9, but it wrong??
 
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  • #2
I am not getting the same answer as you, but I agree that the problem is basically just the Pythagorean Theorem. Check you math again. Do you know what the correct answer is?
 
  • #3


I would like to clarify that the Pythagorean theorem is used to calculate the magnitude of the resulting velocity, not the velocity itself. The velocity is a vector quantity that includes both magnitude and direction.

To calculate the resulting velocity, we can use the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision. In this case, the total momentum before the collision is the sum of the individual momenta of the two cars.

The momentum of the first car, traveling north, can be calculated as 1100 kg x 70 km/h = 77000 kg*km/h in the +j direction. Similarly, the momentum of the second car, traveling west, can be calculated as 2000 kg x (-48 km/h) = -96000 kg*km/h in the -i direction.

When the two cars collide and stick together, their total momentum after the collision will be the same as the total momentum before the collision. Therefore, the resulting velocity can be calculated as the total momentum divided by the total mass of the wreckage.

Total momentum = 77000 kg*km/h + (-96000 kg*km/h) = -19000 kg*km/h

Total mass = 1100 kg + 2000 kg = 3100 kg

Resulting velocity = (-19000 kg*km/h) / (3100 kg) = -6.13 km/h

To find the direction of the velocity, we can use the tangent function to calculate the angle between the velocity vector and the +j direction. The angle can be calculated as arctan(-6.13 km/h / 84.9 km/h) = -4.13 degrees.

Therefore, the magnitude of the resulting velocity is 84.9 km/h and the direction is -4.13 degrees from the +j direction. It is important to note that the negative sign indicates that the direction of the velocity is opposite to the initial direction of the first car.
 

Related to Particle Collision: Cars Collide at Intersection - Magnitude & Direction

1. What is a particle collision?

A particle collision is when two or more particles come into contact with each other, resulting in a transfer of energy and a change in their direction and/or magnitude.

2. How do cars collide at an intersection?

Cars collide at an intersection when they enter the same space at the same time, resulting in a collision. This can happen due to failure to yield, running a red light, or not following traffic signals.

3. What factors determine the magnitude of a car collision?

The magnitude of a car collision is determined by the speed and weight of the vehicles involved, as well as the angle and direction of impact. Other factors, such as road conditions and vehicle safety features, can also play a role.

4. How is the direction of a car collision determined?

The direction of a car collision is determined by the angle at which the two vehicles come into contact with each other. This is often influenced by the direction in which the cars were traveling before the collision occurred.

5. What are the consequences of a car collision?

The consequences of a car collision can range from minor vehicle damage to serious injuries or fatalities. It can also result in legal and financial consequences, such as insurance claims and potential lawsuits.

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