# Horizontal Distance Between Log & Bridge | Homework Statement

• noaamari
In summary, the conversation discusses how to calculate the horizontal distance between a log and a bridge when a stone is dropped from the bridge and lands on the log. The first step is to find the time it takes for the stone to fall 75m using the equation x=1/2*g*t^2. Then, the conversation discusses how to relate this time to the movement of the log, which has a constant speed of 5.0 m/s. Finally, the conversation mentions using another equation to calculate the horizontal distance, but the exact equation is not specified.
noaamari

## Homework Statement

A log is floating on swiftly moving water. A stone is dropped from rest from a 75-m high bridge and lands on the log as it passes under the bridge. If the log moves with a constant speed of 5.0 m/s, what is the horizontal distance between the log and the bridge when the stone is released?

## Homework Equations

Not really sure how to start off the problem, would appreciate if anyone could help me on the problem.

## The Attempt at a Solution

I tried using the equation VF^2=Vi+2a(Xf-Xi)

A good place to start is to find the time it takes for the stone to fall those 75m. How can you relate that time to the movement of the log?

Not really sur how to find the time when the only given information is that it is 75m high from the log. If I need to find the time I also need the velocity or acceleration. So how can I do that?

noaamari said:
Not really sur how to find the time when the only given information is that it is 75m high from the log. If I need to find the time I also need the velocity or acceleration. So how can I do that?

You know the height.

You know gravity.

x = 1/2*g*t2

Okay so i followed the equation and got apporoximately 3.9 secs then what equation can I use next to relate to horizontal distance?

How fast again was the log moving?

## 1. What is the horizontal distance between the log and bridge?

The horizontal distance between the log and bridge is the distance between the two objects measured in a straight line along a horizontal plane.

## 2. How is the horizontal distance between the log and bridge calculated?

The horizontal distance can be calculated using the Pythagorean theorem, where the square of the horizontal distance is equal to the sum of the squares of the vertical and horizontal distances. Alternatively, it can also be measured directly using a measuring tool such as a ruler or tape measure.

## 3. Why is the horizontal distance between the log and bridge important?

The horizontal distance between the log and bridge is important because it can affect the stability and safety of the bridge. If the distance is too small, the bridge may not be able to support the weight of the log, leading to potential collapse. If the distance is too large, it may cause the log to roll off the bridge, posing a danger to anyone crossing it.

## 4. How does the horizontal distance between the log and bridge affect the weight distribution?

The horizontal distance between the log and bridge plays a crucial role in weight distribution. If the distance is not evenly distributed, it can cause the bridge to tilt or become unbalanced, which can lead to structural damage or collapse.

## 5. Can the horizontal distance between the log and bridge change over time?

Yes, the horizontal distance between the log and bridge can change over time due to various factors such as weathering, erosion, and human activities. Regular maintenance and inspection of the bridge are necessary to ensure that the distance remains within safe limits.

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