What Direction Should You Row to Cross a River Straight Across?

[negation]

Homework Statement

You wish to row straight across a 63m wide river. You can row at a steady 1.3 m/s relative to the water, and the river flows at 5.7 m/s. In what direction should you head? How long will it take you to cross the river?

The Attempt at a Solution

Is the answer right? Could the answer equally be 26°?

 

[phinds]

Think about this with simple logic for a minute. The river is flowing downstream at some speed. In order to not be at all swept downstream, the upstream component of your rowing speed relative to the river has to exactly match the downstream speed of the river. Is that possible in this problem?

 

[negation]

Think about this with simple logic for a minute. The river is flowing downstream at some speed. In order to not be at all swept downstream, the upstream component of your rowing speed relative to the river has to exactly match the downstream speed of the river. Is that possible in this problem?

I suppose the answer is 116° instead of 64°.

 

[phinds]

I suppose the answer is 116° instead of 64°.

Are you going to answer my question or just continue to ignore it?

 

[negation]

Are you going to answer my question or just continue to ignore it?

I've already answered it. In rowing at 116° from the x-axis, the boat goes against the current, no?

 

[negation]

I tried solving it from another approach, where;

(1.3ms^-1)^2 = (0.57ms^-1)^2 +y^2
y = 1.168ms^-1
theta = 26°

 

[phinds]

You need to reread my question in post #2. You have not answered it.

 

[haruspex]

Think about this with simple logic for a minute. The river is flowing downstream at some speed. In order to not be at all swept downstream, the upstream component of your rowing speed relative to the river has to exactly match the downstream speed of the river. Is that possible in this problem?

There's a typo in the OP. If you look at the attachment you'll see the river speed is given as 0.57 m/s.
Yes, negation, the answer is 26 degrees to the normal.

 

[phinds]

There's a typo in the OP. If you look at the attachment you'll see the river speed is given as 0.57 m/s.
Yes, negation, the answer is 26 degrees to the normal.

Ah ... well that explains it.

 

[negation]

There's a typo in the OP. If you look at the attachment you'll see the river speed is given as 0.57 m/s.
Yes, negation, the answer is 26 degrees to the normal.

My mistake for the typo. I apologize.
Would that be the same as 116 degrees from the x-axis since it would in other words implies 26 degrees NW.

Edit: I think it is.

 

[negation]

Think about this with simple logic for a minute. The river is flowing downstream at some speed. In order to not be at all swept downstream, the upstream component of your rowing speed relative to the river has to exactly match the downstream speed of the river. Is that possible in this problem?

It's not possible since
v_downwards> v_upwards.
I made a typo in the values.

 

[haruspex]

My mistake for the typo. I apologize.
Would that be the same as 116 degrees from the x-axis since it would in other words implies 26 degrees NW.

Since the OP says nothing about x or y axes, nor about compass directions, that's impossible to answer.
In terms of river bank and direction of flow of river, where were you measuring 116 degrees from?

 

[negation]

Since the OP says nothing about x or y axes, nor about compass directions, that's impossible to answer.
In terms of river bank and direction of flow of river, where were you measuring 116 degrees from?

I measured 116° from the x-axis.
That would put the boat in quadrant 2 but of course since there was no reference point mentioned by the question, it could equally be implied 26° NW, 64° from the x-axis or 26° NE, isn't it?
I have a preference for 116° from the x-axis to do away with all the bearings.

 

[haruspex]

I measured 116° from the x-axis.
That would put the boat in quadrant 2 but of course since there was no reference point mentioned by the question, it could equally be implied 26° NW, 64° from the x-axis or 26° NE, isn't it?
I have a preference for 116° from the x-axis to do away with all the bearings.

I cannot see inside your head. I do not know where your x-axis is, nor which way the river runs in terms of a compass bearing.

 

[negation]

I cannot see inside your head. I do not know where your x-axis is, nor which way the river runs in terms of a compass bearing.

There.

 

[haruspex]

View attachment 65657

There.

Yes - assuming the river is flowing left to right.

 

[Mahmood Abd]

How long will it take?
t=d/v
t=63/1.3=48.5 s
is it correct?
i am comfused since the answer in my textbook tells that t=53.9 s.
please, provide me with explanation.
Regards.

 

[haruspex]

How long will it take?
t=d/v
t=63/1.3=48.5 s
is it correct?
i am comfused since the answer in my textbook tells that t=53.9 s.
please, provide me with explanation.
Regards.

The 1.3m/s is the rowing speed relative to the water. It would take 48.5 s if you were to head straight across, relative to the water. But then you would end up somewhat downstream when you landed. In order to row straight across relative to the riverbank, you have to aim a little upstream. That means some of your 1.3m/s is spent countering the flow of the water.