# Working with two moving targets ?

• maca_404
In summary: But instead of actual distance, you can use the average speed -> total distance / total time. For the bike that would be 80 km/h * (t+5s) = 80t + 400 km. And for the car it would be 100 km/h * t = 100t. Then set them equal, solve for time, and add the acceleration time.
maca_404
Working with two moving targets ??

Hey guys, Here is the question I am working on

"A car traveling at a constant speed of 80kmh passes as stationary motorcycle policeman. The policeman sets off in pursuit, accelerating to 80kmh in 10 seconds and reaching a constant speed of 100kmh in another 5 seconds. At what time will the policeman catch up with the car. "

I have worked this out so far 80 km h–1 = 22.222 m s–1
and 100 km h–1 = 27.778 m s–1

Let the required time = t.

The distance traveled by the policeman in the first 10.0 s
= 0.5(22.222 m s–1)(10 s) = 111.111 m,
and in the next 5.0 s he travels a distance of 0.5(22.222 m s–1 + 27.778 m s–1)(5.0 s)
= 125 m.

When the policeman catches up with the car, it is

(22.222 m s–1)t = 236.111 m + (27.778 m s–1)(t – 15 s)

and so t = 32.5 s.

So I have the correct answer but to find the answer I just used trial an error till I got the correct time. What I want to know is surely there is an easier way to work out the answer without having to take a stab in the dark. I am sure this is probably a simple maths thing but it just keeps eluding me. Any help you can offer would be great.

Thanks

Welcome to PF!

Hi maca! Welcome to PF!

maca_404 said:
So I have the correct answer but to find the answer I just used trial an error till I got the correct time.

hmm … it's good that you can see you did something wrong … your answer just doesn't look neat, does it, and that's usually a sign that it could be improved!

But you didn't use trial and error - you used an equation for t, which is what you're supposed to do:
(22.222 m s–1)t = 236.111 m + (27.778 m s–1)(t – 15 s)
and solved it!

(btw, I haven't actually checked whether it's right)

The "something wrong" is that you put in an unnecessary step - when you wrote:
and in the next 5.0 s he travels a distance of …
you could just as easily have written:
and in the next t s he travels a distance of ….

That would have given you a very similar equation, which already has t in it, giving you the answer more quickly and more neatly!

Write it again, with that change. And then … can you see an alternative way of calculating the second (steady-speeds) patt of the distance?

For the bike to catch up to the car means they've traveled the same distance in the same time. The only difference is in how they did it. The car was traveling at a constant speed while the bike had to accelerate and then travel at a constant speed to catch up.

So if you work out how far the bike went while accelerating and how far the car went in the same time. You can then use $s = x_0 + ut$ for both the car and bike, set them equal and solve for time, then add that to the time when the bike was accelerating. This is pretty much what you've done.

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## 1. What are the challenges of working with two moving targets?

The main challenge of working with two moving targets is the complexity of tracking and coordinating the movements of both targets simultaneously. This requires a high level of coordination and precision in order to avoid collisions or other unwanted interactions.

## 2. How do you account for the movements of both targets in your experiments?

In order to account for the movements of both targets, scientists often use specialized equipment such as motion tracking systems or high-speed cameras. These tools allow for accurate and real-time tracking of the targets' movements, which can then be analyzed and incorporated into the experimental design.

## 3. What are the benefits of working with two moving targets in research?

Working with two moving targets allows for the study of dynamic and complex interactions, which can provide valuable insights into biological, physical, and social systems. It also allows for the testing of hypotheses and theories in a more realistic and ecologically valid setting.

## 4. What types of research fields commonly use two moving targets in their studies?

Fields such as biomechanics, robotics, psychology, and animal behavior often use two moving targets in their research. This is because these fields often involve the study of interactions and movements between multiple objects or organisms.

## 5. How do you control for external variables when working with two moving targets?

To control for external variables, scientists often use control groups, replicate experiments, and carefully design their experiments to minimize the influence of external factors. They may also use statistical methods to analyze and account for any potential confounding variables in their results.

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