Crossing a flowing river problem

[shizupple]

Homework Statement

A hunter wishes to cross a river that is 1.6 km wide and that flows with a speed of 3.4 km/h. The hunter uses a small powerboat that moves at a maximum speed of 12.4 km/h with respect to the water. What is the minimum time necessary for crossing?

Homework Equations

pythagorean theorem
dx=vi(t)

The Attempt at a Solution

I used pythagorean theorem to find the resultant velocity of the water flowing and the speed of the boat:
square root of: 3.4^2+12.4^2= 12.9km/h

Divide width of river by the velocity: 1.6/12.9 = .124hr

Multiply hours by 60 to get mins: .124x60= 7.44 mins

I don't know if i am not getting something right when I'm drawing the picture or if I've understood the problem wrong. Any ideas would be great!

 

[Delphi51]

1.6/12.9 = .124hr has it, except the number given was 12.4 rather than 12.9.

 

[Kelvin Anto]

Hunter wants to cross in shortest time. So he rows his boat in the direction AB .
but river current -> Direction along BC.. so he gets displaced to right & Reaches c. Use Vector concept. He moves along AB with v=12.4km/hr V(river)=3.4km/h
so, V(resultant)= 12.9km/h Time taken by him is not width of river/12.9, But it is t= AC/12.9 t= AB/velocity of boat [because AC= AB/cos θ.& V(resultant)= v(boat)/cos θ
so, cos θ cancels and shortest time is t= AB/v(boat) so, t=1.6/12.4= 0.129hr = 8.14min

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[Cryphonus]

I think this is a little tricky question, there is certainly no effect/time loss because of the current, since the question itself gave you the value of your speed with respect to water and you have the width of the river, you can ignore the rest and do a basic X=velocity.time to solve the question

Let me clarify myself here the speed that makes you move in the vertical direction is naturally your vertical speed, and your horizontal speed (which has no effect on your vertical speed, but it has an effect on your total speed) just causes the displacement in the horizontal way.

 

[ronaldlover]

i strongly agree with your caculations.
ou have done a wonderful and detailed job of explianing this.

 

[shizupple]

I think this is a little tricky question, there is certainly no effect/time loss because of the current, since the question itself gave you the value of your speed with respect to water and you have the width of the river, you can ignore the rest and do a basic X=velocity.time to solve the question

Let me clarify myself here the speed that makes you move in the vertical direction is naturally your vertical speed, and your horizontal speed (which has no effect on your vertical speed, but it has an effect on your total speed) just causes the displacement in the horizontal way.

Ok so your saying the horizontal speed just causes displacement but won't effect the total time to get across the river. You basically disregard the speed of the river. I did the displacement divided by the speed of the hunters boat and got the right answer. I guess its kind of like thinking of it as a gravity problem in disregard to sideways motion.