2-D Kinematics Riverboat problem, finding current strength?

In summary, to find the current speed in the 2-D Kinematics Riverboat problem, we need to use the concept of vector addition and the Pythagorean theorem. By breaking down the boat's velocity relative to the shore into horizontal and vertical components, and considering the motion of the boat relative to the water, we can solve for the current speed, which is equal to the velocity of the water relative to the shore.
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2-D Kinematics Riverboat problem, finding current strength??

Homework Statement



A boat whose spead is 2.20 m/s in still water must cross a 260m river and arrive at a point 110m upstream from where it starts. The boat's pilot has a heading of 45 degrees upstream, what is the current speed?

Homework Equations



sine of the angle = Vbs/Vbw ?

Vbs - velocity of the boat relative to shore
Vbw - velocity of the water relative to shore
Vws - veloicty of the water relative to shore

The Attempt at a Solution



I'm very confused as how to tackle this problem, I started off finding the boat's velocity relative to the shore,

2.20cos45 = 1.56 m/s

Now that I have this I'd assume i could find the river's velocity using pathagorus, but the 45 degree angle and the fact that the boat is to travel in a line to a destination not directly in front of it has thrown me off.

Any pointers would me much appreciated, I'm more than likely missing a crucial step that I can't see..

Cheers.
 
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  • #2


Hello! I can offer some guidance on how to approach this problem. First, it's important to understand the basic principles of 2-D kinematics, which involves the motion of objects in two dimensions (such as horizontal and vertical). In this problem, we are dealing with both horizontal and vertical motion, as the boat is moving across the river and also upstream.

To solve this problem, we need to use the concept of vector addition. This means that the velocity of the boat relative to the shore (Vbs) can be broken down into two components: the horizontal component (Vbx) and the vertical component (Vby).

To find Vbx, we can use the cosine function: Vbx = Vbs*cos(45). Similarly, to find Vby, we can use the sine function: Vby = Vbs*sin(45).

Now, we can use the Pythagorean theorem to find the magnitude of the boat's velocity relative to the shore (Vbs): Vbs^2 = Vbx^2 + Vby^2.

Next, we need to consider the motion of the boat relative to the water. Since the boat is moving at a 45 degree angle upstream, the water must be flowing downstream at the same angle. This means that the boat's velocity relative to the water (Vbw) is equal to the water's velocity relative to the shore (Vws).

Now, we can set up an equation to solve for Vws: Vws = Vbx + Vbw. We know that Vbx = Vbs*cos(45), and we can solve for Vbw by rearranging the equation: Vbw = Vws - Vbx.

Finally, we can plug in the given values to solve for Vws: Vws = 2.20 m/s - 1.56 m/s = 0.64 m/s. This is the velocity of the water relative to the shore, which is also the current speed.

I hope this helps! Let me know if you have any further questions or if you need clarification on any of the steps. Good luck!
 

FAQ: 2-D Kinematics Riverboat problem, finding current strength?

1. How do you determine the velocity of the river current in a 2-D Kinematics Riverboat problem?

In order to determine the velocity of the river current, you will need to first calculate the velocity of the boat relative to the water. This can be done by using the Pythagorean theorem to find the magnitude of the boat's velocity and then using trigonometry to find the direction. Once you have the velocity of the boat relative to the water, you can use vector addition to find the velocity of the boat relative to the ground. The difference between the two velocities will give you the velocity of the river current.

2. What information do I need to solve a 2-D Kinematics Riverboat problem?

To solve a 2-D Kinematics Riverboat problem, you will need to know the boat's velocity relative to the water, the angle of the boat's direction relative to the water, and the distance traveled by the boat. Additionally, you will need to know the time it took for the boat to travel the given distance.

3. How does the direction of the river current affect the boat's motion in a 2-D Kinematics Riverboat problem?

The direction of the river current will affect the boat's motion in a 2-D Kinematics Riverboat problem by changing the direction of the boat's velocity relative to the ground. This will result in the boat traveling a curved path instead of a straight line. The magnitude of the river current's velocity will also affect the boat's overall speed and direction of motion.

4. Can I solve a 2-D Kinematics Riverboat problem without knowing the boat's velocity relative to the water?

No, the boat's velocity relative to the water is a crucial piece of information needed to solve a 2-D Kinematics Riverboat problem. Without this information, you will not be able to accurately determine the velocity of the river current and therefore will not be able to solve the problem.

5. How do I check if my solution to a 2-D Kinematics Riverboat problem is correct?

To check if your solution to a 2-D Kinematics Riverboat problem is correct, you can use the given information to calculate the boat's position at different times and compare it to your calculated solution. Additionally, you can also use the equations of motion to double-check your calculations and ensure they are correct.

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