Aboat that travels 3.00 m/s relative to the water is crossing a river that is 1.00 km wide. the destination on the far side of the river is 0.500 km downstream from the starting point. (a) if the river current is 2.00 m/s, in what direction should the boat be pointed in order to reach the destination? (b) how much time will the trip take?

a) 10.29° upstream

b) t=338.7s

Explanation:

If the river is 1km wide and the destination point is 0.5km away downstream, then the angle and distance the the boat has to travel is:

The realitve velocity of the boat respect to the water is:

 where β is the angle it has to be pointed at.

From the relative mvement equations:

 where

From this equation we get one equation per the x-axis and another for the y-axis. If we square each of them and add them together, we will get 2 equations:

 Solving for V:

V = 3.3m/s   and   V=-1.514m/s   Replacing this value into one of our previous x or y-axis equations:

The amount of time: