Solving an Inelastic Collision: Finding the Angle of Motion for Two Cars

AI Thread Summary
In an inelastic collision between a red car and a blue car, the red car (1000 kg) moving north at 15 m/s and the blue car (1500 kg) moving east at 20 m/s stick together post-collision. The conservation of momentum equations for both x and y components were applied correctly, leading to a common velocity of approximately 12 m/s in the x-direction and 6 m/s in the y-direction. The angle of motion, calculated using θ = tan-1(vfy/vfx), results in approximately 26.57 degrees north of east. The initial confusion about the answer being incorrect was clarified, confirming that the calculated angle is accurate. The discussion emphasizes the importance of applying momentum conservation principles in solving such collision problems.
alexito01
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Homework Statement



A red car and a blue car collide at an in intersection. Prior to the collision the red car with mass 1000kg was heading North at 15m/s. The blue car with mass 1500 kg was heading East at 20m/s. The collision is completely inelastic with the cars sticking together and moving as one. At what angle measured North of East do the cars move off?

Homework Equations


I used Vf = √(Vfx2) + (Vfy2)

I alsoUsed m1vf1x+ m2vf2x= m1vi1x + m2vix for x component and
m1vf1y+ m2vf2y= m1vi1y + m2viy for y component

and then θ = tan-1(vfy/vfx) to findthe angle but i keep geting it wrong

The Attempt at a Solution


I ended up with an angle of around 27 degrees
 
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This is a conservation of momentum problem, not conservation of energy as your title suggests. However, your method looks good and I agree with your answer. What's wrong with it?
 
That is correct about 27 degrees north of east. at a velocity about 13.5 m/s (13 with 2 sig figs)
 
Cars stick after collision. So they have common velocity. Let velocity = vf
Take east as +ve x and north as +ve y

For x component:-
(m1+m2)vfx = m1vi1x + m2vix
(1000+1500)vfx = 1000*0 + 1500*20
2500 vfx = 30000
vfx = 30000/2500 = 300/25
vfx = 12 m/s

For y component
(m1+m2)vfy = m1vi1y + m2viy
(1000+1500)vfy = 1000*15 + 1500*0
2500 * vfy = 15000
vfy = 15000/2500 = 150/25 = 6 m/s

theta = tan-1(vfy/vfx) = tan-1(6/12) = tan-1(1/2) = 26.565 deg
So, as approximation, this is same as your answer. Why do you think your answer is wrong?
 
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