Finding Initial Velocity of a car hit by a train

[Matt4936]

Homework Statement

A train which weighs 1.4406E4N hit a car with a mass of1470kg. The cars skids 15m at angle of 68° to the crossing and the coefficient of friction between the tyres and the road is 0.25. Find the initial velocity of the car entering the crossing.

Homework Equations

Gravitational force = Mass×Gravity
Normal Force = Gravitational force
Friction force = Coefficient of friction ×normal force
F=ma
Vector component equations...

The Attempt at a Solution

I got the acceleration to be -2.45m/s^2 and I was thinking of finding the vertical (north) component of the system using trigonometry which may corespond to the car's velocity but I was wondering what equation I should use to translate the north compotent into the initial velocity. Still I am unsure if that is even right because the north component directly coresponds to the car's frictional force.

Note that I divided the frictional force by the mass to find the acceleration.

 

[LawrenceC]

This problem is vague. Are we to assume the car and train were traveling at right angles prior to the impact? Do we assume the car loses no velocity perpendicular to the train during the collision? Is the collision one where the car bounces off the front of the train so the collision mimics the collision of billard balls?

 

[Matt4936]

Yes, the train and car are traveling at right angles before the collision and the car does bounce off the front of the train and we also do assume that no velocity is lost during the collision. SorryI didn't add this information, I just subconsciously assumed this after looking at the accompanying picture.

 

[Matt4936]

Since I am able to find the initial velocity the moment after the collision; is the velocity of the car before the collision equal to the north component? I get approximately 34m/s.

 

[PhanthomJay]

You are on the right track.
But what did you get for the velocity of the car immediately after impact?

 

[Matt4936]

36.75m/s

 

[PhanthomJay]

How did you arrive at that figure?

 

[Matt4936]

Sorry, I misinterpreted the whole question. The train derails and 'fuses' with the car and I find the momentum and then I find the north component's momentum and then find v from there.

As for how I got 36.75m/s; I mustn't have been thinking properly because I multiplied the distance by the acceleration. I should have used the equation v^2=u^2+2as and I did and found the velocity immediately after impact to be 8.57m/s. I the used that to find the momentum with the masses of both the car and train added together. Also I assumed that the angle was 68° to the road part of the crossing so that I use cosine when finding the momentum of the north component.

In the end I get the initial velocity of the car to be 30.6m/s which I believe is the correct answer.