Officer overtaking soldiers (tricky problem)

  • Thread starter FatheadVT
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In summary, the problem involves an officer inspecting a marching column of soldiers and returning to his starting point. The total distance traveled by the officer can be expressed in terms of the length of the column and the distance advanced during the inspection. The solution may require introducing new variables, but they can be eliminated in the end.
  • #1
FatheadVT
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Homework Statement


I'm completely stumped by a simple sounding problem in my mechanics class. It's not for credit, but I'm frustrated and want to see if I can figure it out with some hints.

A column of soldiers has length L and is marching in a straight line at constant speed. An officer at the tail of the column rides forward to inspect the soldiers and when he reaches the head of the column, he reverses direction and returns to the tail. By the time the officer finishes his inspection, the column has advanced a distance d. What is the total distance traveled by the officer? Assume that the officer's speed is constant throughout the inspection.

Answer should be in terms of L and d.

2. The attempt at a solution

I've thought of everything I can, but I haven't found a way of solving this problem which doesn't introduce new terms such as the velocities of the officer and the soldiers. Any help??
 
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  • #2
FatheadVT said:

Homework Statement


I'm completely stumped by a simple sounding problem in my mechanics class. It's not for credit, but I'm frustrated and want to see if I can figure it out with some hints.

A column of soldiers has length L and is marching in a straight line at constant speed. An officer at the tail of the column rides forward to inspect the soldiers and when he reaches the head of the column, he reverses direction and returns to the tail. By the time the officer finishes his inspection, the column has advanced a distance d. What is the total distance traveled by the officer? Assume that the officer's speed is constant throughout the inspection.

Answer should be in terms of L and d.

2. The attempt at a solution

I've thought of everything I can, but I haven't found a way of solving this problem which doesn't introduce new terms such as the velocities of the officer and the soldiers. Any help??

Adding new variables isn't so bad if you can eliminate them again.
 
  • #3


This is a classic problem in kinematics and can be solved using a simple equation relating distance, speed, and time. The key to solving this problem is to understand that the officer's total distance traveled is equal to the distance traveled while overtaking the soldiers, plus the distance traveled while returning to the tail of the column.

First, let's define some variables:
L = length of the column of soldiers
d = distance advanced by the column during the officer's inspection
v = speed of the soldiers
vo = speed of the officer

We can use the equation d = vt, where d is the distance traveled, v is the speed, and t is the time. We know that the officer travels a distance L while overtaking the soldiers, and then travels a distance L again when returning to the tail. The time it takes for the officer to travel these distances is the same, as the officer's speed is constant throughout the inspection.

So, we can set up the equation:
L = vo*t + vo*t
Solving for t, we get t = L/vo.

Now, we can use this time value to find the total distance traveled by the officer:
Total distance = distance while overtaking + distance while returning
= vt + vt
= v(L/vo) + v(L/vo)
= 2vL/vo

We know that the distance advanced by the column is d, so we can set up another equation:
d = vt
Solving for v, we get v = d/t.

Substituting this value of v into our equation for total distance, we get:
Total distance = 2(d/t)L/vo
= 2dL/vo^2

Therefore, the total distance traveled by the officer is 2dL/vo^2. This solution is in terms of L, d, and the speeds of the officer and the soldiers. I hope this helps you to solve the problem!
 

FAQ: Officer overtaking soldiers (tricky problem)

What is the situation being described in the problem of "Officer overtaking soldiers"?

The situation being described is that of an officer who is trying to overtake a group of soldiers while they are marching in a line. The officer is not able to pass the soldiers due to certain conditions.

What are the possible reasons for the officer not being able to overtake the soldiers?

There can be a few reasons for this, such as the officer being unable to match the speed of the soldiers, the soldiers being too spread out, or the officer being blocked by other obstacles on the road.

What factors should be considered in solving this tricky problem?

To solve this problem, factors such as the speed of the soldiers, the distance between the officer and the soldiers, and the overall terrain should be taken into consideration. Other factors such as the weight and equipment carried by the soldiers can also affect the solution.

What are some possible solutions to this problem?

Some possible solutions include the officer increasing their speed, the soldiers adjusting their pace to allow the officer to pass, the officer taking a different route to overtake the soldiers, or the soldiers creating a gap in their formation to allow the officer to pass.

How can this problem be related to real-life situations?

This problem can be related to real-life situations where a person or vehicle is trying to overtake a larger group or slower-moving object. It can also be seen in emergency response scenarios where emergency vehicles are trying to pass through a crowded road. The problem highlights the importance of cooperation and adaptability in situations where different objects or entities are moving at different speeds.

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