What is the Maximum Horizontal Distance for a Rooftop Escape?

In summary, the problem involves a criminal running off a rooftop at a speed of 5.7 m/s and trying to land on the roof of an adjacent building. The maximum value for the horizontal distance between the two buildings is being sought. Using the equation s=ut + .5at^2, with air resistance being negligible, the time is calculated to be 0.4077 seconds. Multiplying this by the initial speed gives a distance of 2.324 m, but this answer is incorrect. It is discovered that the error was in not taking the square root of (2 x 2)/9.81.
  • #1
xupe33jrm
14
0

Homework Statement


A criminal is escaping across a rooftop and runs off the roof horizontally at a speed of 5.7 m/s, hoping to land on the roof of an adjacent building. Air resistance is negligible. The horizontal distance between the two buildings is D, and the roof of the adjacent building is 2.0 m below the jumping-off point. Find the maximum value for D.


The Attempt at a Solution


s=ut + .5at^2, so t^2 = 2s/g = (2 x 2)/9.81, t=0.4077, then do .4077 x 5.7 = 2.324 m, but that answer is wrong. I have no idea what is going on here, please help.
 
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  • #2


xupe33jrm said:

Homework Statement


A criminal is escaping across a rooftop and runs off the roof horizontally at a speed of 5.7 m/s, hoping to land on the roof of an adjacent building. Air resistance is negligible. The horizontal distance between the two buildings is D, and the roof of the adjacent building is 2.0 m below the jumping-off point. Find the maximum value for D.


The Attempt at a Solution


s=ut + .5at^2, so t^2 = 2s/g = (2 x 2)/9.81, t=0.4077, then do .4077 x 5.7 = 2.324 m, but that answer is wrong. I have no idea what is going on here, please help.

Check your math, did you take the square root of (2 x 2)/9.81?
 
  • #3


It was my math, thanks! I could not figure out what I was doing wrong!
 

What is the purpose of finding the maximum value?

The purpose of finding the maximum value is to determine the highest possible value among a given set of data or numbers. This can be useful in various scientific and mathematical calculations, as well as in making comparisons and identifying trends.

How do you find the maximum value in a data set?

To find the maximum value in a data set, you can use various methods such as sorting the data in ascending order and identifying the last (or largest) value, or using a mathematical formula such as the derivative to find the maximum point on a graph. There are also computer programs and algorithms designed specifically for finding the maximum value in a data set.

Can there be more than one maximum value in a data set?

Yes, there can be more than one maximum value in a data set. This is known as a "tie" or "multiple modes" and occurs when two or more values occur with the same highest frequency. In such cases, all the tied values are considered as the maximum value.

What is the difference between absolute and relative maximum value?

An absolute maximum value is the highest value in a data set without any restrictions or limitations, while a relative maximum value is the highest value within a specific range or condition. For example, in a graph, the absolute maximum value is the highest point on the curve, while the relative maximum value can be the highest point within a certain interval of the x-axis.

How can finding the maximum value be useful in real-world applications?

Finding the maximum value has many practical applications in various fields such as economics, engineering, and medicine. For example, in economics, finding the maximum value of a company's profits can help in decision-making and resource allocation. In engineering, determining the maximum load a structure can withstand is crucial for ensuring safety. In medicine, identifying the maximum dosage of a drug can help prevent overdose and potential harm to patients.

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