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

AI Thread Summary
In a two-car collision scenario, the final velocity can be calculated using momentum conservation principles. The initial momentum for each car is determined by multiplying mass and velocity, leading to equations for the final momentum in both x and y directions. The use of sine and cosine functions is essential for resolving these components, with sine applied to the y-component and cosine to the x-component. Understanding the relationship between mass, velocity, and momentum is crucial, as the final velocity is derived from the total momentum divided by the total mass. Establishing the correct relationships between sides of the triangle formed by the collision is vital for accurate calculations.
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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..
 
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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 accleration:

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.
 
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