What is the magnitude and direction of the wreckage after the collision?

[kh_x2]

The car of mass 1500 kg is traveling east at 25 m/s and collides at an intersection with the truck of 2500 kg mass traveling north at 20 m/s if the wreckage moves as one mass after the collision (the collision is inelastic), calculate the magnitude and direction of the wreckage after the collision.

My problem is that I have used two methods of working the magnitude - both of which are in my notes and both of which give me a different answer and I don't know how to find the direction at all.


Before After
East > North ^ ?
1500 2500 4000
25 20 V

North was weird so I took it as positive ie east aswell

37500 + 50000 = 4000v
v= 87500/4000
v= 21. 875 m/s so it moves east direction


or it will move in west direction at 3.125 m/s if you take north as negative ( this answer is wrong i think)

 

[cryptoguy]

I'm not 100% sure about what you did. I would, for the moment not focus on positives and negatives because you are dealing with vectors that have direction. I believe you figured out the magnitude of the velocity correctly (21. 875 m/s). Now you have to figure out the direction, correct?

You can do this several ways, using trig. You know the x and y component of momentum, so you can figure out the resultant angle which will be the angle at which the object moves.