How Does a Boat's Velocity Change with Current Direction and Speed?

[nocturnalwun]

Consider a boat that travels at 10 km/hr in still (non-moving) water. If the boat travels in a river that flows at a rate of 10 km/hr, what will be its velocity relative to the shore when it heads directly upstream (against the current)? What happens when it heads downstream (with the flow)? Explain




Suppose the boat is oriented at right angles to the water flow and begins moving. Using vector components and vector addition rules, how would you go about finding the direction in which the boat will move relative to the shore? I am interested in the process, not the numerical answer.


This is part of a test I have to take, but i have not been able to purchase the textbook required for the class yet and there is no way for me to figure out how to do these problems

 

[HallsofIvy]

Originally posted by nocturnalwun
Consider a boat that travels at 10 km/hr in still (non-moving) water. If the boat travels in a river that flows at a rate of 10 km/hr, what will be its velocity relative to the shore when it heads directly upstream (against the current)? What happens when it heads downstream (with the flow)? Explain

Think about walking upward on a "down" escalator. It is possible to walk upward at exactly the speed the escalator is moving so that you are not going up or down. On the other hand, if you walk downward while the escalator is moving down, you speed adds to that of the escalator. If your boat moves 10km/hr relative to the water and the water is flowing at 10 km/hr then the speeds add (boat going downstream) and subtract (boat going upstream).
In particular, if the boat moves upstream, relative to the water, at exactly the same speed the water flows relative to the bank, then the boat will have speed 0 relative to the bank.

If the boat is moving at right angles to the flow of the river, then you can think of this as a right triangle. Draw a leg of the triangle across the river with length the same as the speed of the boat. Draw a leg of the triangle in the direction of flow (at right angles to the first leg) with length the same as the speed of the river. The length of the hypotenuse will give the speed of the boat relative to the bank. Do you know how to find that? Do you know how to find the angles in the triangle?

 

[M98Ranger]

Sure, I would be happy to help with your questions. Let's start with the first question about the boat's velocity relative to the shore when it heads directly upstream (against the current). In this scenario, the boat's velocity relative to the shore would be 0 km/hr. This is because the boat's velocity is equal to the water's velocity (10 km/hr) but in the opposite direction, resulting in a net velocity of 0 km/hr.

When the boat heads downstream (with the flow), its velocity relative to the shore would be 20 km/hr. This is because the boat's velocity (10 km/hr) is added to the water's velocity (10 km/hr) in the same direction, resulting in a net velocity of 20 km/hr.

Now, for the second question about finding the direction in which the boat will move relative to the shore when it is oriented at right angles to the water flow. To determine this, we can use vector components and vector addition rules. First, we would need to break down the boat's velocity into its horizontal and vertical components, using trigonometry. Then, we would add these components to the water's velocity components, using vector addition rules. This would give us the boat's net velocity relative to the shore, and the direction in which it will move can be determined from this net velocity vector.

I hope this explanation helps you understand the process of solving these types of problems. I understand that it can be challenging without the textbook, but there are also many online resources and videos that can help you with vector addition and trigonometry. Good luck with your test!