Hi, I am having trouble with one physics problem I would like to have some help,

Question

Hi, I am having trouble with one physics problem I would like to have some help, please and thanks in advance.

The problem:

Car A is travelling from the left, horizontally, with a velocity of 20 m/s. Car B is travelling from the right with a velocity of 10(2) m/s, at an angle of 45 above the horizontal. Car A has a mass of 350kg while the mass of car B is 300kg. The two cars make a perfectly in-elastically collision(they stick together).

a) give the final momentum vector magnitude and the direction. Indicate degrees, left-right and above-below the horizontal

b)give the velocity of the system after the collision, in the most simplified form?

Explanation / Answer

Hi, so the easiest way to do this problem is by finding the total momentum of the system. 

I reccomend drawing parts as you go. Visulaizing problems makes everything easier.

Find the vertical and horizontal componets of speed of the moving Car B from the angle you are given.  Once you have these multiply by the respective masses to get the momentum of Car A and the momentum of Car B in the horizontal direction and vertical direction.  (or for Car B find the total momentum then split this up using the angle given into horizontal and vertical components)

Now sum your momentums for the horizontal and verticle components. (Vertical is easy since Car A isn't moving in that direction).  Remember you need a negative sign for Car be since its moving in the opposite direction.

With the two momentum components you just calculated you can construct a right triangle to get the final overall momentum and you can use the Tangent trig function to get the angle/direction. 

For part B since you have the momentum you can now divide by the TOTAL mass to get the final velocity.  The direction does not change if you need that as well.  (Not sure what is meant by "in the most simple form").

When it comes to problems like this always draw it out.  Find Right Triangles if you can, they make it easy to separate comenents and add vectors easily.

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