Solving Collision Question: Speed After Intersection Impact

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In a collision between two identical cars traveling at 50 km/h, one north and one east, the correct method to determine the speed of the wreck after impact involves conserving momentum rather than simply applying the Pythagorean theorem. The initial momentum of the system must be calculated by considering both cars' velocities and masses, as they become locked together post-collision. The misconception that the speed can be directly calculated as 70.7 km/h arises from incorrectly combining velocities without accounting for mass. To solve the problem accurately, the total momentum before the collision should equal the total momentum after the collision, allowing for the calculation of the final velocity of the combined wreck. Understanding momentum conservation is crucial for solving such collision questions effectively.
eclipse30
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I've been working on this question and I just don't know how to arrive at the correct answer!
Here's my question.

Two identical cars, each traveling at 50km/h, one traveling north and one traveling east, collide at an intersection and become locked together.
What is the speed of the joint wreck immediately after the collision?


I tried using the pythagoras theorum to attempt finding the new speed.
Root(50^2 + 50^2) but this gave me a new speed of 70.7km/h which I believe is wrong since the are moving at a faster speed.

How do I solve this question?:confused:
 
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Since the external forces that act on the system (the two cars) sum to zero, the linear momentum of the system is conserved. So you have the final total momentum of the system set equal to the initial total momentum of the system. Now you can solve for the final velocity.
 
eclipse30 said:
I tried using the pythagoras theorum to attempt finding the new speed.
Root(50^2 + 50^2) but this gave me a new speed of 70.7km/h which I believe is wrong since the are moving at a faster speed.
As hotcommodity explained, you should be adding the momentum, not just the velocities. (You can still use this calculation, but you'll have to modify it to include the mass.) When the cars are locked together, what's the total mass?
 

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