Find the angle the boat has to head

In summary, the problem involves a boat traveling at a speed of 8.2 m/s in still water, crossing a river with a current of 4.5 m/s and a width of 477 meters. The heading of the boat needs to be adjusted in order for it to land 100 m upstream from the starting point. The solution involves thinking of the problem as a triangle and adjusting the angle and speed of the boat accordingly. In real life, adjustments would need to be made constantly to reach the desired destination.
  • #1
Goopy17
39
0

Homework Statement


A boat, which can travel at 8.2 m/s in still water, heads directly across a river which has a current of 4.5 m/s and is 477 meters wide. What should the heading of the boat be in order for it to land at a point on the opposite shore exactly 100 m upstream from the starting point?


Homework Equations


Not sure


The Attempt at a Solution


I really don't know where to start
Thanks for the help!
 
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  • #2
I'd think of it as a triangle. You have the speed across (8.2 m/s), the base 477 m and the speed along the short side 4.5 m/s. That's the geometry answer, but it's simple.
Of course, in the real world you just keep adjusting the boat to get to the point you want to go. You start off, realize your going down stream, and adjust your angle upstream to compensate. You change your speed a lot too, but that's the real world of boats.
 

FAQ: Find the angle the boat has to head

1. What is the purpose of finding the angle the boat has to head?

Finding the angle the boat has to head is important for navigation and determining the direction in which the boat needs to be steered. This helps ensure the boat reaches its intended destination efficiently and safely.

2. How do you calculate the angle the boat has to head?

The angle the boat has to head can be calculated using trigonometry, specifically the tangent function. The angle can be found by dividing the opposite side (distance to travel) by the adjacent side (distance from the boat to the destination).

3. What factors influence the angle the boat has to head?

The angle the boat has to head is influenced by various factors such as wind direction and speed, water currents, and the boat's speed and size. These factors can impact the boat's ability to maintain a straight course, requiring adjustments to the angle.

4. Can digital tools be used to find the angle the boat has to head?

Yes, there are various digital tools and instruments that can be used to determine the angle the boat has to head. These include GPS devices, compasses, and navigation software that can calculate the angle based on the boat's current location and destination.

5. How does finding the angle the boat has to head differ in different bodies of water?

The angle the boat has to head may differ in different bodies of water due to varying conditions such as wind patterns, current strength, and obstacles. Additionally, the boat's heading may also need to be adjusted to account for the curvature of the Earth in large bodies of water.

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