What Angle Should a Boat Point Upstream to Cross a River Straight?

[agadag]

Homework Statement

A boat that can travel at 4.0 km/h in still water crosses a river with a current of 1.8 km/h. At what angle must the boat be pointed upstream to travel straight across the river? In other words, in what direction is the velocity of the boat relative to the water?

1. 27° upstream
2. 33° upstream
3. 37° upstream
4. 39° upstream

Homework Equations

V= D/T?

The Attempt at a Solution

i found a problem similar in the book but the answer doesn't make any sense. I have an exam over this material tomm and would really apppreciate if someone can demonstrate and help me understand the solution!

 

[rl.bhat]

Show your calculations.

 

[tomcue]

I can provide a mathematical solution to this problem. The velocity of the boat relative to the water can be calculated using vector addition. The velocity of the boat in still water is 4.0 km/h in the direction of the boat's travel, while the velocity of the current is 1.8 km/h in the direction of the river flow. These two velocities can be added using the Pythagorean theorem to find the resultant velocity of the boat relative to the water. This resultant velocity can then be used to calculate the angle at which the boat must be pointed to travel straight across the river.

Using the equation V = d/t, we can set up the following equation:

4.0 km/h = √(1.8 km/h)^2 + V^2

Solving for V, we get a resultant velocity of 3.8 km/h. This means that the boat must be pointed at an angle of 37° upstream in order to travel straight across the river.

To further explain this, imagine the boat is traveling at a 37° angle upstream. The component of its velocity in the direction of the river flow (1.8 km/h) will cancel out the current, leaving only the component of its velocity in the direction of the boat's travel (3.8 km/h). This allows the boat to travel straight across the river.

I hope this helps you understand the solution better. Good luck on your exam!