# Time and velocity

## 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?

andrevdh
Homework Helper
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?

lisab
Staff Emeritus