Speed, Displacement, and Velocity Question

[Jordan_]

Homework Statement

A boat, propelled so as to travel with a speed of 0.50m/s in still water, moves directly across a river that is 60m wide. The river flows with a speed of 0.30m/s. (a) At what angle, relative to the straight across direction, must the boat be pointed? (b) How long does it take the boat to cross the river?

Answer: (a) 37 degrees upstream (b) 1.5x10^2 seconds.

Homework Equations

pythagorean theorem

The Attempt at a Solution

I tried to use the movement of the boat at 0.50m/s with the 60m across and found that that would take 120 seconds. Then, I multiplied the 120 seconds by the river current speed of 0.30m/s to find that it would pull the boat 36 meters downstream. Then I tried to find the angle using tan(theta) = opp/adj but I got the angle 31 degrees.

I tried several other methods last night that I can't remember now, and I kept getting 31 degrees. The book states that it is 37 degrees, however, and so I'm wondering what I'm doing wrong.

 

[hage567]

I tried to use the movement of the boat at 0.50m/s with the 60m across and found that that would take 120 seconds.

This isn't correct because the boat's velocity will have two components to it since it must head at an angle due to the river current. You will need to figure out the component that is perpendicular to the river for part (b).

So don't worry about using the distance just yet. Draw your vectors first. You know the direction and speed of the river, and you know the speed the boat can go relative to the still water. So if the boat is to land directly across from its starting point, you know the boat must be initially pointing upstream at some angle. Adding these two vectors must give a vector that goes straight across the river. So draw a triangle based on this, and you can solve for the angle.