Finding the resultant velocity?

Click For Summary

Homework Help Overview

The discussion revolves around determining the resultant velocity of a boat moving north across a river while being affected by an eastward current. Participants are exploring the relationship between the boat's velocity and the current, specifically focusing on calculating the resultant velocity and the angle relative to the bank.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of the resultant velocity using the Pythagorean theorem and question how to determine the angle to the bank. There are inquiries about the assumptions regarding the boat's direction relative to the riverbanks and the necessity of a diagram for clarity.

Discussion Status

The discussion is active, with participants offering insights and questioning assumptions. Some suggest that the angle can be found using trigonometric functions, while others emphasize the importance of direction in velocity. There is no explicit consensus on the interpretation of the problem setup.

Contextual Notes

Participants note that the problem does not explicitly state that the boat's path is perpendicular to the bank, leading to varied interpretations of the scenario. The lack of provided equations or additional conditions is also mentioned.

Math9999

Homework Statement


A boat heads north across a river at a rate of 4 miles per hour. If the current is flowing east at a rate of 3 miles per hour, find the resultant velocity of the boat.

Homework Equations


None.

The Attempt at a Solution


I know that the resultant velocity is the hypotenuse, which means that 4^2+3^2=v^2, where v=5 mi/h. And that's only part of the answer. The whole answer in the textbook says 5 mi/h at an angle of ≈53.13° to the bank. But how do I find the angle to the bank?
 
Physics news on Phys.org
Math9999 said:

Homework Statement


A boat heads north across a river at a rate of 4 miles per hour. If the current is flowing east at a rate of 3 miles per hour, find the resultant velocity of the boat.

Homework Equations


None.

The Attempt at a Solution


I know that the resultant velocity is the hypotenuse, which means that 4^2+3^2=v^2, where v=5 mi/h. And that's only part of the answer. The whole answer in the textbook says 5 mi/h at an angle of ≈53.13° to the bank. But how do I find the angle to the bank?
Not without additional assumptions or conditions. You need to interpret "across the river" as perpendicular to the banks.
 
Math9999 said:

Homework Statement


A boat heads north across a river at a rate of 4 miles per hour. If the current is flowing east at a rate of 3 miles per hour, find the resultant velocity of the boat.

Homework Equations


None.

The Attempt at a Solution


I know that the resultant velocity is the hypotenuse, which means that 4^2+3^2=v^2, where v=5 mi/h. And that's only part of the answer. The whole answer in the textbook says 5 mi/h at an angle of ≈53.13° to the bank. But how do I find the angle to the bank?

Have you drawn a diagram?
 
  • Like
Likes   Reactions: Math9999
Well, the problem didn't mention as perpendicular to the bank. So that means the answer is just 5 mi/h, right?
 
Math9999 said:
Well, the problem didn't mention as perpendicular to the bank. So that means the answer is just 5 mi/h, right?

A velocity always has a direction.
 
  • Like
Likes   Reactions: Math9999
So how to figure the angle out?
 
Math9999 said:
So how to figure the angle out?
By the assumption I've suggested and the diagram @PeroK has suggested. Figure out the remaining angles of your triangle.
 
  • Like
Likes   Reactions: Math9999
cos-1(3/5)≈53.13°, am I right?
 
Math9999 said:
cos-1(3/5)≈53.13°, am I right?

I suspect your calculator can tell you that!
 
  • #10
Okay, thank you!
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 16 ·
Replies
16
Views
4K
Replies
10
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
24
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K