Ball Thrown between Trains
Date: 10/15/2003 at 03:09:36 From: Juily Subject: trains Two trains A and B each of length 100m travel in opposite directions in parallel tracks. The speeds are 20m/s and 30m/s respectively. A boy sitting in the front end of train A throws a ball to a boy sitting in the front end of train B when they are at the closest distance. The speed of the ball is 2m/s. The ball, instead of reaching the boy, hits the rear end of the train. Find the distance between the parallel tracks. I am confused as to whether I should take the vector component of the speed of train A and the ball. I do not have an answer to the question to verify my answer with.
Date: 10/15/2003 at 07:22:23 From: Doctor Luis Subject: Re: trains Hi Juily, The ball will obtain a parallel component equal to 20 m/s, which is the speed of the train A, and a perpendicular component equal to 2 m/s, which is the speed at which the boy threw the ball. Now, when I say parallel and perpendicular components, I mean relative to the track. Here's a diagram representing the situation at t = 0, the time when the boy threw the ball Let the position of the ball at time t = 0 be x = 0, y = 0. That is, define the origin at that point in time. What is the position of the ball at time t = T secs, when the ball hits the back of train B? Well, the x-component traveled at +20m/s, and the y-component traveled at +2m/s, so we have x = (20 m/s)T y = (2 m/s)T But at time t = T, we know that the ball hit the back of train B. What does this mean? Well, the ball made it to the other track, so this means that y = H, the separation between the tracks. Also, we know that after T seconds, the front of train B traveled 30T meters to the left. This means the back of the train, which started at x = +L (since the train is L meters long), must now be at x = L - 30T. Since these are the coordinates of the ball, we must satisfy the equations (20 m/s)T = L - (30 m/s)T (2 m/s)T = H Using the first equation, you can solve for T using the train length L = 100 m. And once you know T, you can finally find H, what the problem asked for. I hope this helped! Let us know if you have any more questions. - Doctor Luis, The Math Forum http://mathforum.org/dr.math/
Date: 10/15/2003 at 08:32:25 From: Juily Subject: Thank you (trains) Hi Dr. Luis, Thank you for your time and for such a quick response. I think that all of you are doing a great job. Looking forward to asking you more questions, Juily
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