# Solving River Crossing: Angle for Boat Rowing Across River

• totororain
In summary, the problem involves a person crossing a river with a maximum velocity of 6.835 km/hr relative to the water. The river flows at a rate of 2.147 km/hr. To reach the opposite shore directly across from the starting point, the person must point the boat at an angle of 43.39 degrees with respect to a line perpendicular to the river shore. The direction of the boat's pointing should be indicated with a negative or positive sign for upstream or downstream, respectively. The solution can be found using vector decomposition and the formula cos(data) = Ax/A.
totororain

## Homework Statement

A person in a rowboat crosses a river which flows with 2.147 km/hr. The person rows with maximum velocity of 6.835 km/hr relative to the water (measured while rowing on a still lake) and wants to reach the opposite shore directly across from the start point - along a line at 90 degrees with respect to the river shore . At what angle with respect to this line does the person have to point the boat (sheet 15 to 16")? Indicate with a negative (positive) sign whether the boat has to be pointed upstream (downstream).

## The Attempt at a Solution

I'm not sure how to solve this, but i used the vector decomposition, 43.39 degree . . . i used the forumula [cos(data) = Ax/A]

Please anyone, help me out asap thank you so much...i need help urgently!

Last edited:
Your answer and formula don't make sense to me, could you explain them? Draw a diagram of the situation, putting all known values and directions on it, then try again (it should look like a triangle).

Vector decomposition should work, you want the the boat to travel upstream (or downstream) at a rate equal and opposite to the river flow, so that the sideways velocity components cancel each other out. Thus you know what the opposite will be and you already know the hypotenuse. From that you can find the angle and also the component of velocity across the stream.

Last edited:
Welcome to PF!

totororain said:
I'm not sure how to solve this, but i used the vector decomposition, 43.39 degree . . . i used the forumula [cos(data) = Ax/A]

Hi totororain ! Welcome to PF!

Sorry, but your answer and formula don't make sense to me either.

You need to show us exactly how you got to 43.39 … then we can see how to help you!

## What is the "River Crossing: Angle for Boat Rowing Across River" problem?

The River Crossing: Angle for Boat Rowing Across River problem is a mathematical puzzle that involves determining the optimal angle at which to row a boat across a river to minimize the distance traveled. It is commonly used as a problem in mathematics and physics classes to teach students about vectors and optimization.

## What is the significance of solving this problem?

The significance of solving this problem lies in its applications in real-world situations. By determining the optimal angle for boat rowing across a river, we can save time and energy, and make more efficient use of resources. This problem is also a good exercise for developing critical thinking and problem-solving skills.

## What are the key factors to consider when solving this problem?

The key factors to consider when solving the River Crossing: Angle for Boat Rowing Across River problem include the width of the river, the speed of the current, the speed of the boat, and the angle at which the boat is rowed. Additionally, the problem may also involve taking into account obstacles or other factors that may affect the path of the boat.

## What are some common approaches to solving this problem?

There are several common approaches to solving the River Crossing: Angle for Boat Rowing Across River problem. These include using vector analysis to determine the shortest distance, using trigonometry to calculate the optimal angle, or using calculus to find the minimum of the distance function. Other approaches may involve creating a mathematical model and using computer simulations to find the optimal solution.

## How can solving this problem be applied to real-life situations?

The problem of determining the optimal angle for boat rowing across a river has many real-life applications. For example, it can be used in navigation to determine the most efficient route for a boat to travel, or in engineering to design more efficient water transportation systems. Additionally, the problem can also be applied to other scenarios, such as finding the shortest path for a vehicle to travel through a city with one-way streets or avoiding obstacles.

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