Can You Solve This Inelastic Collision Problem Without All Variables?

[phy]

Hi everyone. I need some help with the following question.

In a traffic accident, a car of mass 2000kg traveling south collided in the middle of an intersection with a truck of mass 7000kg traveling west. The vehicles locked and skidded off the road long a line pointing southwest. A witness claimed that the truck had entered the intersection at 80km/hour.
a) Do you believe the witness? Why/why not?
b) Find the velocities of the vehicles before and after the collisions in the centre of mass frame.
c) How much kinetic energy is lost in the collision?

My problem is that I think there are too many values that are not given. I tried using the equation m1v1+m2v2 = (m1+m2)v' but then I didn't know what values to use for v1 and v'. Does anybody have any thoughts on this?

 

[e(ho0n3]

Yes, it would seem the problem is unsolvable unless you know: the velocity of the car, the velocity of the combined car/truck after collision, or another equation relating these quantities.

 

[wais]

Firstly, in order to determine if the witness is credible, we would need to know the credibility of the witness and if there were any other witnesses or evidence to support their claim. Without this information, it is impossible to say whether or not the witness is telling the truth.

As for the question of finding the velocities, we can use the conservation of momentum equation, m1v1 + m2v2 = (m1+m2)v', where m1 and m2 are the masses of the car and truck respectively, v1 and v2 are the initial velocities, and v' is the final velocity in the centre of mass frame. We can also use the fact that the vehicles lock and skid off the road in a southwest direction to determine the direction of the final velocity.

However, as you mentioned, there are several values that are not given. We would need at least one more piece of information, such as the final velocity or the coefficient of restitution, in order to solve for the final velocities.

As for the kinetic energy lost in the collision, we would also need to know the initial and final velocities in order to calculate the change in kinetic energy. Without this information, we cannot accurately determine the amount of energy lost in the collision.

In summary, without more information, it is difficult to solve this problem accurately. It would be helpful to have at least one more piece of information, such as the final velocity or the coefficient of restitution, to solve for the final velocities and the amount of energy lost in the collision.