Fisherman's boat Relative motion

In summary: No.b) how far downstream he will be before he reaches the other shore (300 m)I was thinking the ground velocity is 2.5m/s...In summary, a fisherman can cross a river in 200 seconds if he does not drift downstream, and he will be 300 meters downstream from the bank before he reaches the other shore.
  • #1
heythere1010
36
0

Homework Statement


A fisherman wishes to cross a river to the shore directly south of his position. The river is 400 m across, and the fisherman's boat is capable of a speed of 2.5m/s. If the river's current has a velocity of 1.5m/s [W], determine

a) the time it takes the fisherman to cross the river (200 s)
how far downstream he will be before he reaches the other shore (300 m)

This is the part I didn't answer.

If the fisherman wished to land on the shore directly south of his position, how long would it him take to cross the river, and what would be the ground velocity of the boat?

Homework Equations


d =v*t

The Attempt at a Solution


I have calculated the time from question 1, but I'm not sure what is different about time in question 2. I was thinking the ground velocity is 2 m/s since it would be d/t.
 
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  • #2
How did you calculate the 200 second answer for a)?

Edit: Scratch that. I see how you got 200 seconds. How did you get 300 meters?
 
  • #3
jbriggs444 said:
How did you calculate the 200 second answer for a)?

Edit: Scratch that. I see how you got 200 seconds. How did you get 300 meters?
I made a triangle with 2.5m/s as the hypotenuse, 1.5m/s as one of the sides. and solved for the other side. I did t=d/v (400/2=200).
 
  • #4
Right. Now how did you get 300 meters?
 
  • #5
jbriggs444 said:
Right. Now how did you get 300 meters?
1.5(200)
 
  • #6
And what is 1.5?
 
  • #7
jbriggs444 said:
And what is 1.5?
Velocity of the current.
 
  • #8
Is it the same as the downstream velocity of the boat?
 
  • #9
jbriggs444 said:
Is it the same as the downstream velocity of the boat?
No.
 
  • #10
The question asks how far downstream the boat goes, not how far downstream the current goes. So multiplying by 1.5 would not be appropriate. But let's back up and re-examine what the question is asking...

heythere1010 said:

Homework Statement


A fisherman wishes to cross a river to the shore directly south of his position. The river is 400 m across, and the fisherman's boat is capable of a speed of 2.5m/s. If the river's current has a velocity of 1.5m/s [W], determine

a) the time it takes the fisherman to cross the river
how far downstream he will be before he reaches the other shore

If the fisherman wished to land on the shore directly south of his position, how long would it him take to cross the river, and what would be the ground velocity of the boat?
As I read this, there are two parts with two questions each.

The first part (which you answered) assumes that the fisherman aims his boat due south relative to the moving water. So it drifts downstream at the same rate as the current. The second part (about which you are asking) assumes that the fisherman aims his boat at an angle so that his boat does not drift downstream.

If this is the case, what is the boat's southward velocity for the first part?
 
  • #11
jbriggs444 said:
The question asks how far downstream the boat goes, not how far downstream the current goes. So multiplying by 1.5 would not be appropriate. But let's back up and re-examine what the question is asking...As I read this, there are two parts with two questions each.

The first part (which you answered) assumes that the fisherman aims his boat due south relative to the moving water. So it drifts downstream at the same rate as the current. The second part (about which you are asking) assumes that the fisherman aims his boat at an angle so that his boat does not drift downstream.

If this is the case, what is the boat's southward velocity for the first part?
Yes. I calculated the angle in another part of the question. I got 53 degrees.
 
  • #12
Are you assuming that the boat's ground speed is 2.5 meters per second or that the boat's speed with respect to the water is 2.5 meters per second? The problem assumes the latter.

53 degrees is not consistent with the intended interpretation of the problem.
 
  • #13
jbriggs444 said:
Are you assuming that the boat's ground speed is 2.5 meters per second or that the boat's speed with respect to the water is 2.5 meters per second? The problem assumes the latter.

53 degrees is not consistent with the intended interpretation of the problem.
The boat's speed is 2.5m/s
 
  • #14
jbriggs444 said:
The first part (which you answered) assumes that the fisherman aims his boat due south relative to the moving water.
That's not how I understand it. It says, "A fisherman wishes to cross a river to the shore directly south of his position. I understand this to mean he lands (not aims) directly south.

heythere1010 said:
a) the time it takes the fisherman to cross the river (200 s)
Did you get this time assuming he aims south? Can you show how you got the time?

heythere1010 said:
I was thinking the ground velocity is 2 m/s since it would be d/t.
That's one way to do it, since it's constant. I'm not exactly sure what you did to get the time. I found the time from the relative velocity. And this is the time I get for landing south, not aiming south.
 
  • #15
Nathanael said:
That's not how I understand it. It says, "A fisherman wishes to cross a river to the shore directly south of his position. I understand this to mean he lands (not aims) directly south.
That's how I read it at first as well. But the existence of the second part of the question makes that interpretation untenable.
 
  • #16
jbriggs444 said:
That's how I read it at first as well. But the existence of the second part of the question makes that interpretation untenable.
Or it could be a simple conceptual question not intended to be calculated.
 
  • #17
Nathanael said:
Or it could be a simple conceptual question not intended to be calculated.

The numbers are too carefully chosen for that interpretation to be tenable.
 
  • #18
I made a triangle with 2.5m/s as the hypotenuse, 1.5m/s as one of the sides. and solved for the other side. I did t=d/v (400/2=200). That's how I solved time.
 
  • #19
jbriggs444 said:
The numbers are too carefully chosen for that interpretation to be tenable.
Why's that? The speed of the boat is more than that of the river.
 
  • #20
And that's the wrong approach for the first part. 2.5 m/s is not the hypotenuse.
 
  • #21
heythere1010 said:
I made a triangle with 2.5m/s as the hypotenuse, 1.5m/s as one of the sides. and solved for the other side. I did t=d/v (400/2=200). That's how I solved time.
Why is 2.5 the hypotenuse? 2.5 m/s is the speed of the boat relative to water, not relative to the shore.
 
  • #22
It's a 3-4-5 triangle. That's an unlikely coincidence.
 
  • #23
jbriggs444 said:
It's a 3-4-5 triangle. That's an unlikely coincidence.
No coincidence necessary; it's not a real fisherman. Are you saying it's impossible for the boat to reach the shore directly south of where it started?
 
  • #24
Nathanael said:
No coincidence necessary; it's not a real fisherman. Are you it's impossible for the boat to reach the shore directly south of where it started?
Certainly it's possible. But that's not what part 1 is asking for. Part 2 asks about reaching the point on the shore due south. And that's where the original 3-4-5 triangle comes in.
 
  • #25
Nathanael said:
Why is 2.5 the hypotenuse? 2.5 m/s is the speed of the boat relative to water, not relative to the shore.
So do I just do 400/2.5(his speed)?
 
  • #26
heythere1010 said:
So do I just do 400/2.5(his speed)?
To find the time aiming south, yes.
 
  • #27
Yes. It is just that simple. His southward velocity is 2.5 meters per second and he needs to cover 400 meters southward.
 
  • #28
How about for the second part of finding the time?
 
  • #29
heythere1010 said:
How about for the second part of finding the time?
Now you can draw that right triangle. But label the sides to keep track of what each one represents.

First, the southward pointing side. This is the southward component of the boat's velocity relative to the water.

Next the eastward (or westward) pointing side. This is the upstream component of the boat's velocity relative to the water. This must be 1.5 meters per second in order to avoid driving upstream or drifting downstream.

Finally the hypotenuse. This is the boat's total velocity relative to the water. Its length is given by the max speed of the boat, 2.5 meters per second.

You had already solved this triangle for the southward velocity represented by the unknown side.
 
  • #30
so this is how I did it, I think it makes sense
 

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1. What is relative motion in a fisherman's boat?

Relative motion in a fisherman's boat refers to the movement of the boat in relation to its surroundings. This can include the motion of the boat in the water, the motion of the water itself, and the motion of other objects in the water such as fish or other boats.

2. How does relative motion affect a fisherman's boat?

Relative motion can affect a fisherman's boat in a number of ways. For example, if the boat is moving in the same direction as the current, it will experience less resistance and may move faster. On the other hand, if the boat is moving against the current, it will experience more resistance and may move slower.

3. How can a fisherman use relative motion to their advantage?

A fisherman can use relative motion to their advantage by understanding how it affects the movement of their boat and the water around them. For example, they can position their boat in a spot where the current is moving in their favor, making it easier to navigate and potentially increasing their chances of catching fish.

4. What is the difference between relative motion and absolute motion?

The main difference between relative motion and absolute motion is that relative motion takes into account the movement of objects in relation to each other, while absolute motion refers to the movement of objects in relation to a fixed point or frame of reference. In the case of a fisherman's boat, relative motion would be the movement of the boat in relation to the water and other objects, while absolute motion would be the movement of the boat in relation to a specific point on the shore or a GPS location.

5. How can understanding relative motion help with fishing techniques?

Understanding relative motion can help with fishing techniques by allowing fishermen to predict the movement of fish and other objects in the water. For example, if a fisherman knows that fish tend to swim against the current, they can position their bait or lure accordingly to increase their chances of catching fish. Additionally, understanding how the boat's motion affects the water around it can help with casting and navigating the boat in a more efficient manner.

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