# Physics Boat Problem involving velocity

1. Oct 26, 2007

### sympathy2

1. The problem statement, all variables and given/known data
1. A river that is 209 m wide flows due east at a uniform speed of 2.2 m/s. A boat with a speed of 8.3 m/s relative to the water leaves the south bank pointed in a direction 30° west of north.
(a) What is the magnitude of the boat's velocity? (m/s)
(b) What is the direction of the boat's velocity relative to the ground? (answer in degrees west of north)
(c) How long does the boat take to cross the river? (s)

3. The attempt at a solution
For part a, I tried a few answers such as 16.6, 7.188, 7.2, 4.15, 7.19, but none of those answers were right. I think my main problem is understanding the question, perhaps i misunderstood the "relative to the water" part. Can someone please explain it to me. The right answer would also be appreciated.

2. Oct 26, 2007

### mjsd

"relative to the water" means in the reference frame of the water. note the water is moving "relative to the ground" (or as seen in the frame of the ground). but if you are IN the ref frame of water, then the "ground is moving" instead. as a result, the velocity relative to water would be different from the velocity relative to the ground, for example.