Help Check My Homework: Two Boats & Passenger Speed

In summary, the conversation is about a problem involving two boats and a passenger walking on one of the boats. The boats are heading away from shore, with Boat 1 heading due north at a speed of 3 m/s relative to the shore. Boat 2 is moving 40° north of east at a speed of 1.7 m/s relative to Boat 1. The passenger on Boat 2 walks due east across the deck at a speed of 1.1 m/s relative to Boat 2. The goal is to determine the speed of the passenger relative to the shore. The solution involves setting up vectors for each object's movement and using the Pythagorean theorem to calculate the speed of the passenger, which is approximately
  • #1
YummyPotato
1
0
I tried looking at the other threads on this but they seem incomplete.
I would like someone to check my work.

Homework Statement


Two boats are heading away from shore. Boat 1 heads due north at a speed of 3 m/s relative to the shore. Relative to Boat 1, Boat 2 is moving 40° north of east at a speed of 1.7 m/s. A passenger on Boat 2 walks due east across the deck at a speed of 1.1 m/s relative to Boat 2. What is the speed of the passenger to the shore?


Homework Equations


x and y vectors.


The Attempt at a Solution


I set up vectors for each moving object.

B1x = 0 B2y = 0

B2x = 1.7cos(40°) B2y = 1.7sin(40°)

Px = 1.1 Py = 0

I added the x and y components

Rx = 0 + 1.302 + 1.1 Ry = 0 + 1.09 + 0

= 2.402 = 1.09

Sp^2 = (2.402)^2 + (1.09)^2
Sp ≈ 4.74 m/s.
 
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  • #2
If those vectors are the velocities relative to the shore, then surely B1x=0 and B1y=3 m/s ? ( y being East).
 
  • #3
Mentz114 said:
If those vectors are the velocities relative to the shore, then surely B1x=0 and B1y=3 m/s ? ( y being East).

Don't you mean y being N?
 
  • #4
haruspex said:
Don't you mean y being N?
On re-reading the question, yes, I mean North.
 
  • #5


I would first commend the student for their attempt at using vector equations to solve this problem. It is clear that they have a good understanding of vector components and how to add them to find the resultant vector. However, I would suggest that they label their vectors more clearly to avoid any confusion. For example, instead of using B1x and B2y, they could label them as V1x and V2y to indicate that they are the x and y components of the velocity vectors for Boat 1 and Boat 2, respectively.

Additionally, I would suggest that they draw a diagram to better visualize the problem and the directions of the boats and the passenger's movement. This can also help in labeling the vectors correctly.

Furthermore, I would advise the student to double-check their calculations, as there may be some rounding errors in their final answer. It is always good practice to double-check your work, especially in physics and math problems.

Overall, the student has shown a good understanding of vector components and how to use them to find the resultant vector. With some minor adjustments and double-checking, their solution should be correct.
 

What is the purpose of "Two Boats & Passenger Speed" homework?

The purpose of this homework is to practice solving problems related to relative speed, time, and distance in a real-world scenario involving two boats and their passengers.

How do I approach solving this homework?

First, identify the given information, such as the speeds of the boats and the distances they travel. Then, use the appropriate formulas to calculate the time it takes for each boat to reach their destination and the distance between them. Finally, use the information to solve for the relative speed and the time it takes for the boats to meet.

What are the key concepts that I need to understand for this homework?

To successfully complete this homework, you should have a good understanding of relative speed, time, and distance. You should also be familiar with the formulas for calculating these values, such as the formula for relative speed (V1 + V2) and the formula for time (D/R).

What are some common mistakes to avoid when solving this homework?

Some common mistakes to avoid include using the wrong formula, substituting the wrong values, and not paying attention to units of measurement. It's also important to carefully read and understand the given information and make sure all calculations are accurate.

How can I check my work for accuracy?

You can check your work by double-checking your calculations, making sure the units of measurement are consistent, and using logic to verify your answers. You can also use a calculator or ask a classmate or teacher to review your work.

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