Conservation of Momentum problem

[Arooj]

Homework Statement

A 1500-kg car is traveling north at 25 m/s when it strikes a 2000-kg car traveling east at 20 m/s. The cars stick together after the collision. What is the final velocity of the two cars?

Homework Equations

m1v1 + m2v2 = (m1 + m2)vf

The Attempt at a Solution

1500(25) + 2000(20) = (1500 + 2000)vf
vf = 22.14 m/s

The answer was incorrect. I then thought vectors would be needed but wasn't sure. Can someone guide me through this problem?

 

[haruspex]

You've used the formula as for scalars, which assumes all movement is in the same dimension. Yes, it's a vector question. Treat NS and EW separately.

 

[Arooj]

Thanks, I did so and found the final velocity to be 15.66 m/s. I'm confused on how to find the correct angle to use though for the direction is it the tan x comp over the y comp or the other way around? And how would you know which one it is?

 

[haruspex]

I'm confused on how to find the correct angle to use though for the direction is it the tan x comp over the y comp or the other way around? And how would you know which one it is?

It is standard to give priority to NS, so you should specify the angle as a deviation, E or W, from one of those. That means the tan of the angle will be x over y, in contrast to normal mathematics. You can check whether you have it the right way round by simply seeing which component is the greater and whether the angle is more or less than 45 degrees.