How Long Until Two Cars Collide?

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To determine the time until two cars collide, one must consider their combined speeds and the distance between them. Car A travels east at 30 meters per second, while Car B travels west at 20 meters per second, resulting in a total approach speed of 50 meters per second. Given that they are 400 meters apart, the time until collision can be calculated by dividing the distance by their combined speed, which is 400 meters divided by 50 meters per second. This results in an answer of 8 seconds for the time until the two cars collide. The initial misunderstanding stemmed from incorrectly equating the distances traveled by each car instead of summing them.
drunkenfool
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I understand that this is a REALLY simple question, but for the life of me, I cannot figure out how to get the right answer.

"Two cars, A and B, are 400. meters apart. Car A
travels due east at 30. meters per second on a
collision course with car B, which travels due
west at 20. meters per second. How much time
elapses before the two cars collide?"

Hopefully, some of you helpful souls out there can help me out. I hope no ridicule comes from this. :(

What I have done is find out how much time Car A would take to travel 400 M.
400/30 = 13.333 s

Now I know that they WILL collide atleast before 13.333 s. Other than that, I'm stuck. Thanks in advance.
 
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Ah, oh my God. I know why I didn't get the right answer now. I've been putting 20t = 30t. It had never occurred to me that 20t + 30t is equal to 400. Damn, I feel stupid now.
 
It happens some time. :smile:
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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