Regents Question

Classical Mechanics Level 1

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, in seconds?


The answer is 8.

Hobart Pao by Hobart Pao , 23, USA

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2 solutions

Azadali Jivani
Jan 28, 2015

In 1 sec. both the cars cover a distance of 50 meters (30+20). So 1 meter in ....1/50sec Therefore 400 meter in ........1/50*400 = 8 sec (Ans.)

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I made a system of equations because everything I do is overcomplicated

Hobart Pao - 6 years, 4 months ago
Caleb Townsend
Feb 18, 2015

One car's speed relative to the other's is ( 30 + 20 ) m s = 50 m s . (30 + 20)\frac{m}{s} = 50\frac{m}{s}.
The distance between them is 400 m . 400 m.
Therefore the time to collision is 400 m 50 m / s = 8 s \frac{400 m}{50 m/s} = \boxed{8 s} Note that if the information the asker gave us is correct, they will collide in 8 8 seconds; in real life, hopefully someone moves out of the other's way.

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