# Time and velocity

1. Feb 4, 2008

### jelly1500

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
t=x/v

3. 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?

2. Feb 4, 2008

### andrevdh

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.

3. Feb 4, 2008

### jelly1500

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?

4. Feb 4, 2008

### lisab

Staff Emeritus
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.

5. Feb 5, 2008

### andrevdh

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.