# Time & Velocity Homework: Swimming Across a River

• jelly1500
In summary, the problem involves a swimmer with a speed of 2.0 mi/hr swimming perpendicularly to the bank of a river flowing at the same speed. The river is 1.0 mi wide and the question is how long it takes for the swimmer to reach the other side. The solution involves decomposing the swimmer's motion into two perpendicular components and solving for the time it takes to cover 1.0 mi at a speed of 2.0 mi/hr. The answer is 0.45 hours or 27 minutes.
jelly1500

## Homework Statement

A person who can swim at 2.0 mi/hr is swimming perpendicularly to the bank of a river (directly across the direction of river flow) which is flowing at 2.0 mi/hr. If the river is 1.0 mi wide, how long does it take to reach the other side?

t=x/v

## The Attempt at a Solution

I drew a right triange: the first being 2 mi/hr (the direction of the river flow) and the second being 2mi/hr (the person swimming to the bank) and tried to solve for the hypotenuse through Pythagoreans theorem. Then used t=1/2.83 but it was incorrect. I think I'm drawing the figure wrong?

The resultant motion of the swimmer can be decomposed into two perpendicular independent motions - one with the speed of the swimmer across the river and the other with the speed of the river along the direction of the river. When he has reached the opposite embankment the perpendicular component "covered" a distance 1.0 mi at a speed of 2.0 mi/hr.

Ok, I'm still a little confused. So now I have set up one of my legs on my right triangle as 2 mi/hr for the direction of the water flow, and the other leg as 1.0 mile for the distance he covered. Then I solved for the resultant vector: square root of 2^2 + 1^2, which equals 2.24. Then I plugged it into the time equation, x=1, v=2.24 and got 0.45. Am I on the right track?

I think you had it right the first way you did it. Is the answer given in minutes? Because the time you calculated (t=1/2.83=0.35) is in hours. Convert it to minutes to see if you have the correct answer.

You can approach this problem similar to how the motion of a projectile is analyzed. That is the resultant motion is described by two separate motions - one in the x- and another in the y-direction. For the swimmer it is in one across the river and another along the river. To solve this problem you need only look at the component across the river. The swimmers component in this direction covers one mile at a constant speed of 2 mi/hr when the actual swimmer crosses over to the other side.

## 1. What is the formula for calculating time and velocity in swimming across a river?

The formula for calculating time and velocity in swimming across a river is Time = Distance/Velocity. This means that the time it takes to cross the river is equal to the distance divided by the velocity.

## 2. How does the current of the river affect the time and velocity of swimming across it?

The current of the river can impact the time and velocity of swimming across it as it can either aid or hinder the swimmer's progress. If the current is flowing in the same direction as the swimmer, it can increase their velocity and decrease their time. However, if the current is flowing in the opposite direction, it can slow down the swimmer's velocity and increase their time.

## 3. Is it easier to swim across a river with or against the current?

It is generally easier to swim across a river with the current as it can provide a boost to the swimmer's velocity. However, this also depends on the strength of the current and the swimmer's swimming abilities.

## 4. How can one calculate the velocity of the current when swimming across a river?

The velocity of the current can be calculated by measuring the distance the swimmer travels in a specific amount of time and then using the formula Velocity = Distance/Time. This will give the average velocity of the swimmer and the current combined. To find the velocity of the current alone, the swimmer can repeat the measurement while swimming in the opposite direction and subtract their average velocity from the combined velocity.

## 5. Can the angle at which a swimmer crosses a river affect their time and velocity?

Yes, the angle at which a swimmer crosses a river can impact their time and velocity. A swimmer crossing the river at a 90-degree angle will have a shorter distance to travel and may experience a slower current compared to a swimmer crossing at a 45-degree angle. This can result in a faster time and higher velocity for the swimmer crossing at a 90-degree angle.

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