# Motion, with Two Objects.

• blooreema
In summary, the problem involves two cyclists leaving from different towns at different speeds. To find where they will meet, we can treat them as one bike traveling at a combined speed of 35 km/h for a distance of 20 km. Using the formula speed = distance / time, we can calculate the time it takes for them to meet, and then use that to find the meeting point between the two towns.

#### 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)?

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.

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.

## 1. What is "Motion, with Two Objects"?

"Motion, with Two Objects" refers to the movement of two objects in relation to each other. This can include objects moving in the same direction, opposite directions, or at different speeds.

## 2. How is the motion of two objects measured?

The motion of two objects is typically measured using distance and time. The distance each object travels and the time it takes to travel that distance can be used to calculate their motion, such as speed and velocity.

## 3. What factors can affect the motion of two objects?

The motion of two objects can be affected by various factors such as the mass of the objects, the force applied to them, and any external forces acting on them (such as friction or gravity).

## 4. Can two objects have the same speed but different velocities?

Yes, two objects can have the same speed but different velocities. Velocity takes into account the direction of motion, while speed only measures the rate of motion. So, if two objects are moving at the same speed but in different directions, their velocities will be different.

## 5. How does Newton's Laws of Motion apply to the motion of two objects?

Newtons's Laws of Motion can be applied to the motion of two objects to explain how they move and interact with each other. For example, Newton's First Law states that an object will remain at rest or in motion unless acted upon by an external force, which can be observed in the motion of two objects when no external forces are present.