# Solving Two-Object Motion Problems

• Illicitsky
In summary, two people start from towns 195 miles apart and travel towards each other on the same road. The first person drives 5 miles slower than the second person. Using the equation d=rt, we can set up a chart to solve the problem. We know that the two people meet after 3 hours and the second person's speed is 3 miles per hour faster than the first person's. By setting up equations for the distance each person travels and equating them, we can solve for their individual speeds.
Illicitsky

## Homework Statement

1. Two people leave from two towns that are 195 miles apart at the same time and travel along the same road toward eah other. The first person drives 5 miles slower than the second person. If they meet in 3 hours, at what rate of speed did each travel?

d= rt

## The Attempt at a Solution

Simple motion problems are easy. But HOW do we figure out problems when two objects are going down the same road/path, with X miles in between or even 'overtake' the other?

No idea where to start. Tried to set up d=rt chart by there's too many variables in the problem (the 3 hours thing, then 5 miles slower?)

There are two towns, A and B, D distance apart. There are two people: the first starting from A with speed va, the other starts from B with speed vb=va-3.

Denote the distance of the people from A by xa and xb. At the beginning, xa=0, xb=D

After t time elapsed, the first man is xa=vat distance from A. The other man is xb=D-vbt distance from A.

When they meet, they both are at the same distance from A: xa=xb.

ehild

I can provide a few steps to help solve this type of problem. First, we need to identify the known information and what we are trying to solve for. In this case, we know the distance between the two towns (195 miles), the time it took for them to meet (3 hours), and the fact that one person is driving 5 miles slower than the other. We are trying to find the rate of speed for each person.

Next, we can use the equation d=rt to create two equations, one for each person's distance traveled. Let's call the rate of speed for the first person r and the rate of speed for the second person r+5 (since they are traveling 5 miles faster).

Person 1's distance traveled: d=rt
Person 2's distance traveled: d=(r+5)t

Since they are traveling towards each other, their combined distance will equal the distance between the two towns (195 miles). So we can set up an equation with this information:

195 = (r+5)t + rt

Now we have two equations with two unknowns (r and t). We can solve for one of the variables and then use that value to solve for the other variable.

Let's start by solving for t:

195 = (r+5)t + rt
195 = rt + 5t + rt
195 = 2rt + 5t
195 = t(2r+5)
t = 195/(2r+5)

Now we can substitute this value for t into either one of the original equations to solve for r. Let's use the first equation:

Person 1's distance traveled: d=rt
195 = r(195/(2r+5))
195 = 195r/(2r+5)
2r+5 = 195r/195
2r+5 = r
5 = r

So we have found that the first person was traveling at a rate of 5 miles per hour and the second person was traveling at a rate of 10 miles per hour (since they were going 5 miles per hour faster).

In summary:

Person 1: r=5 miles per hour
Person 2: r+5 = 5+5 = 10 miles per hour

I hope this helps! Remember, when solving two-object motion problems, it's important to identify the known information, set up equations using the

## 1. What are two-object motion problems?

Two-object motion problems are physics problems that involve the motion of two objects, such as two cars moving towards each other or a ball being thrown and caught by two people. These problems usually require the use of equations and principles of motion to determine the position, velocity, or acceleration of each object at a given time.

## 2. How do I approach solving a two-object motion problem?

The first step in solving a two-object motion problem is to identify what is known and what is unknown. This can be done by reading the problem carefully and making a list of all the given information. Then, use the appropriate equations and principles of motion, such as Newton's laws or the kinematic equations, to solve for the unknown variables.

## 3. What are some common mistakes to avoid when solving two-object motion problems?

One common mistake is forgetting to consider the direction of motion. In two-object motion problems, it is important to pay attention to the direction in which the objects are moving, as this can affect the calculations. Another mistake is using incorrect equations or not setting up the equations properly. It is important to understand the principles of motion and choose the appropriate equations for the given problem.

## 4. How can I check my answer for a two-object motion problem?

To check your answer, you can use the equations of motion to calculate the position, velocity, and acceleration of each object at different points in time. Then, compare these values to your calculated values to see if they are consistent. It can also be helpful to double-check your calculations and make sure you used the correct units.

## 5. Can two-object motion problems be solved without using equations?

In most cases, equations and principles of motion are necessary to solve two-object motion problems. However, some problems may provide enough information for you to make an educated estimate of the answer. For example, if you know the initial and final positions of an object, you can estimate the average velocity without using equations. However, using equations will provide a more precise and accurate answer.

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