How Do Two Cyclists Traveling Towards Each Other Meet?

[blooreema]

I tried for a really long time to try to answer this question, but I keep getting weird answers... could someone try and help me out? I know we're supposed to use the substitution method but I don't quite get how...


Vectorville and Scalartown are 20.0 km apart.
A cyclist leaves Vectorville and heads for Scalartown at 20.0 km/h.
A second cyclist leaves Scalartown for Vectorville at exactly the same time at a speed of 15.0 km/h.

a) Where will the two cyclists meet between the two towns?
b) How much time passes before they meet (in minutes)?

 

[lavalamp]

I'm not really sure what you mean by the substitution method, if you were to explain what you mean by that maybe I could give you a pointer as to how to calculate the answer that way.

However, the way I would do it would be to realize that the two bikes could be treated as one bike traveling at 35 Km/h for a distance of 20 Km. Using good old speed = distance / time would give you the answer to part b, then you could use that to calculate the answer to part a.

 

[Moetasim]

I understand your frustration with trying to solve this problem. The key to understanding motion is to break it down into smaller, more manageable pieces. In this case, we have two objects, the two cyclists, moving towards each other at different speeds.

To solve this problem, we can use the concept of relative velocity. This means that we can consider one cyclist as stationary and the other as moving towards them. So, let's say the first cyclist is stationary and the second cyclist is moving towards them at a combined speed of 20.0 km/h + 15.0 km/h = 35.0 km/h.

Now, we can use the formula distance = speed x time, to determine how far the second cyclist travels in the time it takes for them to meet the first cyclist. Since we know the distance between the two towns is 20.0 km, we can set up the equation as 20.0 km = 35.0 km/h x time. Solving for time, we get 20.0 km / 35.0 km/h = 0.57 hours.

To convert this to minutes, we multiply by 60, giving us 0.57 hours x 60 minutes/hour = 34.2 minutes. This is the amount of time it takes for the two cyclists to meet between the two towns.

As for where they will meet, we can use the same formula to determine the distance from Vectorville. Since the first cyclist is stationary, we can say that they have traveled 0 km, and the second cyclist has traveled 35.0 km in 0.57 hours. This means that they will meet 35.0 km away from Vectorville.

I hope this helps you understand the concept of relative velocity and how to solve this type of motion problem. Remember to always break it down into smaller pieces and use the appropriate formulas. Keep practicing and you will become more confident in solving these types of problems.