Collision at Intersection: Calculating Direction & Distance

• joemama69
In summary: Your name]In summary, the conversation discusses a physics problem involving a collision between two cars at an intersection. The final velocity and direction of the wreckage after the collision are calculated, and the coefficient of kinetic friction and distance traveled are also discussed. After some corrections are made to the equations, the correct distance is calculated and found to be approximately 0.01 miles.
joemama69

Homework Statement

Note the picture...

11. Two cars approach an intersection as shown. Car 1 weighs 4500
lbs and has a speed of 55.0 mi/hr. Car 2 weighs 3750 pounds with
a speed of 60.0 mi/hr. They collide in a completely inelastic collision at the intersection.

a) Calculate the direction the wreckage moves after the collision. Express this as an angle measured counterclockwise from the positive x-axis.

b) If the coefficient of kinetic friction is 0.55 for the tires on this road, and the wheels of the car are locked (not rolling), calculate the distance the wreckage slides from the collision point.

The Attempt at a Solution

mc1 = 140slug vca = 55i
mc2 = 116.63 s vc2 = -30i + 51.96j

m1vc1 + m2vc2 = (m1+m2)v'

140(55i) + 116.63(-30i + 51.96j) = (140 + 116.63)v'

v' = 16.37i + 23.61j...theta = 55.26 degreees

Part B

|v'| = 28.73 mph

.5mv2 = ugmd...5v2 = ugd
.5(28.73) = (.55)(9.8)d...d = 2.67

im pretty sure myt last equation is wrong considering it says they slid 2 miles.. ugmd must not be correct, can i get some help

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For part A, you have correctly calculated the final velocity of the wreckage after the collision as (16.37i + 23.61j) mph. To find the direction of this velocity, we can use the inverse tangent function (arctan) to calculate the angle counterclockwise from the positive x-axis. The arctan of 23.61/16.37 is approximately 55.26 degrees, which matches your answer.

For part B, you are on the right track with your equation of .5mv^2 = ugmd, but there are a few things to consider. First, we need to convert the final velocity from mph to m/s, as the coefficient of friction (u) and the acceleration due to gravity (g) are typically given in SI units. So, v' = (28.73 mph)(0.447 m/s/mph) = 12.85 m/s.

Next, we need to consider the fact that the wheels of the car are locked and not rolling. This means that the kinetic friction coefficient (u) should be replaced with the static friction coefficient (us). The equation then becomes .5mv^2 = usgmd.

Additionally, the distance traveled (d) should be measured from the point of collision until the wreckage comes to a complete stop, not from the collision point to the end of the road. This will likely result in a shorter distance.

Putting all these factors together, we can calculate the distance as: .5(140 + 116.63)(12.85)^2 = (0.55)(9.8)d...d = 16.58 meters or approximately 0.01 miles. This is a much more reasonable distance for a collision between two cars.

I hope this helps with your calculations. Let me know if you have any further questions.

?

Thank you for providing this information and your attempt at a solution. As a scientist, my response would be to first check your calculations and equations to ensure they are correct. It is also important to consider any assumptions made in the problem and make sure they are valid. For example, is the collision truly completely inelastic? Are there any external forces acting on the cars?

Additionally, it is important to provide units for all values and to convert them to a consistent system (such as SI units) for accurate calculations.

For the first part, it is important to note that the angle given is measured counterclockwise from the positive x-axis, so the angle should be 180 - 55.26 = 124.74 degrees. This means the wreckage moves in the direction of 124.74 degrees counterclockwise from the positive x-axis.

For the second part, it seems that your calculation for the distance the wreckage slides is incorrect. It is important to consider the initial velocities and the final velocity, as well as any external forces acting on the cars. It may also be helpful to draw a diagram and use the equations of motion to solve for the distance. Additionally, the distance given in the problem is in miles, so it may be helpful to convert all values to miles before solving for the distance.

In conclusion, it is important to carefully consider all information given in the problem and to double check calculations and assumptions to ensure an accurate solution.

1. How is the direction of a collision at an intersection calculated?

The direction of a collision at an intersection is typically calculated using the direction of travel of each vehicle involved in the collision. This can be determined by examining the damage to the vehicles and the location of debris at the scene, as well as eyewitness accounts and surveillance footage.

2. What factors are considered when calculating the distance of a collision at an intersection?

The distance of a collision at an intersection is determined by several factors, including the speed of the vehicles involved, the point of impact, and the location of any skid marks or debris. The type of vehicles and road conditions may also be taken into account.

3. How important is it to accurately calculate the direction and distance of a collision at an intersection?

Accurately calculating the direction and distance of a collision at an intersection is crucial in determining fault and liability. This information can also help reconstruct the sequence of events leading up to the collision and provide valuable evidence in legal proceedings.

4. Are there any tools or methods used to assist in calculating the direction and distance of a collision at an intersection?

Yes, there are various tools and methods that can be used to assist in calculating the direction and distance of a collision at an intersection. These include accident reconstruction software, laser measurement devices, and mathematical formulas based on physics principles.

5. Can the direction and distance of a collision at an intersection be accurately determined without eyewitnesses or surveillance footage?

In some cases, the direction and distance of a collision at an intersection can still be accurately determined without eyewitnesses or surveillance footage. This may be done through the analysis of physical evidence and data such as vehicle damage, skid marks, and road conditions. However, eyewitness accounts and surveillance footage can provide valuable additional information and should always be considered if available.