# Relative Velocity Problem

A boat is traveling 3 m/s relative to the water due north. A current is flowing 4 m/s due east. What is the velocity of the boat relative to the earth? The length of the river is 1000 m. Ok so I used pythogorean theorem and got 5 m/s. Then how would you find the time it takes for the boat to travel the 1000 m? Would it be 3t = 1000, and $t = 333 sec$? This is because you are only looking at the y-component? You couldnt do 5t = 1000?

Thanks

## Answers and Replies

It depends which way the river runs, if the river runs vertically then 3t=1000 would be correct, however this would be assuming that the east flowing current does not push the boat into the bank and that if the boat does have to turn to avoid crashing into the bank then this takes no time.

If the river runs along the hypotenuse then 5t=1000 would be correct, however this would be assuming that the boat does not resist the east flowing current in any way. If there is no other information in the question i think this is the most probable case.