Crossing a River: Boat Problem with Perpendicular Motion

[AnthonyC]

"The river is 50.0 m wide, and flows east at 3 m/s. A boat that can travel on still water at 5 m/s heads in a direction that allows it to cross the river perpendicular to the shore."

Based on this wording, this is the diagram that I came up with, though I really am very unsure as to if it is correct or not.
http://www.recklesscaution.com/riverboat.jpg

I searched online, and all the examples I could find had the problem not indicating that the boat ends up with a perpendicular motion.

Did I assume correctly? Or just goof up again?

 

[OlderDan]

"The river is 50.0 m wide, and flows east at 3 m/s. A boat that can travel on still water at 5 m/s heads in a direction that allows it to cross the river perpendicular to the shore."

Based on this wording, this is the diagram that I came up with, though I really am very unsure as to if it is correct or not.
http://www.recklesscaution.com/riverboat.jpg

I searched online, and all the examples I could find had the problem not indicating that the boat ends up with a perpendicular motion.

Did I assume correctly? Or just goof up again?

It's not quite right. Apart from East usually being to the right instead of down the way you have drawn it the boat's speed in still water would have to be more than 5 m/s

 

[AnthonyC]

I just figured it was neater to have the entire diagram roated 90degrees clockwise.

What do I need to change for it to be correct?

 

[DaveC426913]

Older Dan's got it. In your diagram, you've got the label "5 m/s" on the wrong line. Remove it from the "actual path (horizontal) line" and put it on the "direction traveled (oblique) line" and you'll be all set.

 

[AnthonyC]

Great, thankyou!

I wasn't sure which line it should have been on, so I casually put it between the two, haha.

 

[AnthonyC]

I believe that I have answered these questions correctly:

Direction of the boat relative ot the river:
b) tanθ = (opposite/adjacent)
tanθ = (3/4) = 36.9 degrees

The boat will be heading NW at an angle of 36.870˚

Boat's Velocity
c) a2 = c2 - b2 = √(25 – 9) = 4 m/s

Time taken to cross the river
d) time = distance/(ave. speed)
time = 50m/4m/s = 12.5 s

Can somebody verify? Thanks again!

 

[OlderDan]

I believe that I have answered these questions correctly:

Direction of the boat relative ot the river:
b) tanθ = (opposite/adjacent)
tanθ = (3/4) = 36.9 degrees

The boat will be heading NW at an angle of 36.870˚

Boat's Velocity
c) a2 = c2 - b2 = √(25 – 9) = 4 m/s

Time taken to cross the river
d) time = distance/(ave. speed)
time = 50m/4m/s = 12.5 s

Can somebody verify? Thanks again!

Looks good except for some notation

tanθ = (3/4)
θ = ArcTan(3/4) = 36.9 degrees

The boat will be heading West of North at an angle of 36.870˚ (by your diagram- crossing the river from South to North)

 

[AnthonyC]

Oops, my bad, I'm still used to the social studies version of north/south coming first.

 

[Pyrrhus]

Anthony, it used to happen the same to me when i took Physics I and Surveying I, it was quite confusing, they use the NW which meant West of North, heh.

 

[OlderDan]

Anthony, it used to happen the same to me when i took Physics I and Surveying I, it was quite confusing, they use the NW which meant West of North, heh.

Do they also use NW for a reference for arbitrary directions? I don't know the surveyer's convention. There is nothing ambiguous about NW by itself being 45 degrees West of North, and nothing ambiguous about other cardinal points like SSW and NSW, but when you have directions in between you have to know the convention. What reference directions do they use?

 

[Pyrrhus]

The N Angle W and other combinations are called "directions" ("Rumbo" in spanish) and are taken in reference to the y axis, they help represent a Acimut (North or South) pointing the same way.