How Do You Calculate Final Velocity in a Two-Car Collision Scenario?

[D-X69]

I dropped outta school due to financial problems, after 4 years I finally returned back to school and sadly I had to start over some basics of physics(the worst thing about it is they're not in English and in Chinese instead, I'm an asian of course but I grew up speaking english), which I have completely forgotten. I came across this problem with two cars colliding with each other.

Unfortunately the question's in Chinese. And I'd try my best to translate it.

A car 1500kg traveling east at a speed of 25m/s collide with another car(2500kg) traveling north at a speed of 20m/s. Find V final.

So basically, they'd end up moving north east. And that'd be the V final in a y/x graph.

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The answer is:


Px initial = 1500 x 25 = 37500kg.m/s
Px final = (4000).Vfinal.Cos(theta)

Px intial = Px final

(1) Hence, 37500 = (4000kg).V final . Cos(theta)


Py inital = 2500 x 20 = 4000kg.m/s
py final = (4000kg).vf.sin(theta)

(2) Hence, 4000kg.m/s = (4000kg).vf.sin(theta)

Then make (2) = (1)

Then u get, tan(theta) = 50000/37500

theta = 53.1 degrees

To find Vf:

Vfinal = 50000/(4000).sin53.1degrees = 15.6m/s

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My problems are:

- I sucked at trigonometry functions, I do not get why you'd use sin or cos when finding Px final and Py final. Though I know, Sin = Opp/hyp and Cos = Adj/hyp. So basically if I get similar questions in my previous exams I just tend to use both sin on car A and cos on car B, without knowing the theory behind it.

- So far the first problem didn't made me lose my marks in exam though, my main mistake is, near the end in the solution I've given, I don't get why, mass has to multiply with sin 53.1.

I know for fact V final = momentum/mass

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I hope I addressed my problem clear enough for y'all to assist me. Thanks in advance..

 

[Ambidext]

Fortunately you're asian- we're taught in my country to remember sine/cosine functions with the phrase "toa cah soh" (big foot woman). Here's how we've been trained to remember which function to use:

TOA: Tangent X = Opposite / Adjacent
CAH: Cosine X = Adjacent / Hypotenus
SOH: Sine X = Opposite / Hypotenus

So if I may draw your attention to a typical inclined plane problem, where mass m slides down a slope of inclination angle X, and you're asked to find the mass's acceleration:

We take g to be the hypotenus, the normal force should be the adjacent side to the angle, and the resultant acceleration of the mass should be the opposite side.

Thus, using SOH, acceleration = g sin X

Hope that was helpful to you.


EDIT: I think perhaps you should firmly establish which are the adjacents, opposites and hypotenuses first. Then apply sin/cos formulae.