River bank problem Need help ly

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In summary, the problem involves finding the direction and distance downstream that a person will be carried by a river while trying to deliver a package across it. The river has a constant speed of 2.50 m/s and is 80.0 m wide. The person can only swim at a speed of 1.50 m/s. The solution involves using equations for time and velocity, and possibly using derivatives.
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meulin
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River bank problem! Need help urgently! :(

Homework Statement


The water in a river flows uniformly at a constant speed of 2.50 m/s between parallel banks 80.0 m apart. You are to deliver a package directly across the river, but you can swim only at 1.50 m/s. If you choose to minimize the distance downstream that the river carries you, in what direction should you head? How far downstream would you be carried?

Homework Equations


yf = yi + vt + (1/2)a(t^2)
xf = xi + vt + (1/2)a(t^2)

The Attempt at a Solution


I tried to find the direction initially with this diagram from my answer key (posted below), until I realized that my answer key must be wrong because the Vs, which they indicated as the hypotenuse, is actually less than Vw, which they marked as one of the sides. I wasn't sure what to do, but I'm aware that I probably have to use derivatives in order to find it... however, I'm rather rusty at calculus as I haven't taken it in a while, so I have no idea where to start; if someone could walk me through it step by step, it would be greatly, greatly appreciated!

Thank you so much for your time and help!

P.S. Here is the picture of the diagram from my answer key:

1z4eo9i.png
 
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  • #2


I would start by writing an equation for the time taken to cross.

Then write one for the velocity at which you will travel downstream.

Then come back if you can't work out what to do next.
 

What is the "River Bank Problem"?

The "River Bank Problem" is a classic mathematical puzzle that involves transporting a group of objects from one side of a river to the other using a limited number of trips on a small boat. The goal is to find the most efficient way to move all the objects without leaving any behind.

Why is the "River Bank Problem" important?

The "River Bank Problem" is important because it is a practical application of mathematical problem-solving skills. It also helps develop critical thinking and logic skills, which are useful in many areas of science and technology.

What is the history behind the "River Bank Problem"?

The "River Bank Problem" was first described by the Greek mathematician Archimedes in the 3rd century BC. It has since been studied and solved by many mathematicians, including Leonhard Euler and Édouard Lucas in the 18th and 19th centuries, respectively.

What are some common strategies for solving the "River Bank Problem"?

Some common strategies for solving the "River Bank Problem" include the "greedy" algorithm, which involves always choosing the most optimal option at each step, and the "divide and conquer" approach, which breaks the problem down into smaller, more manageable parts.

How can the "River Bank Problem" be applied in real life?

The "River Bank Problem" has practical applications in transportation and logistics, as well as in fields such as computer science and game theory. It can also be used as a teaching tool to develop problem-solving skills and critical thinking in students.

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