Crossing a River: Boat Direction and Time Calculations

[nealh149]

A 200-m-wide river has a uniform flow speed of 1.1 m/s through a jungle and towards the east. An expoere wishes to leave a small clearing on the south band and cross the river in a powerboat that moves at a constant speed of 4 m/s with respect to the water. There is a clearing on the north band 82 m upstream from a point directly opposite the clearing on the south bank. (a) In what direction must the boat be pointed to travel in a straight line and land in the clearing. (b) How long will the boat take to cross the river?

I've done tons of things to try to solve this from pathagreon theorem to sines and cosines and I cannot solve this for the life of me. Please help.

 

[geoffjb]

A 200-m-wide river has a uniform flow speed of 1.1 m/s through a jungle and towards the east. An expoere wishes to leave a small clearing on the south band and cross the river in a powerboat that moves at a constant speed of 4 m/s with respect to the water. There is a clearing on the north band 82 m upstream from a point directly opposite the clearing on the south bank. (a) In what direction must the boat be pointed to travel in a straight line and land in the clearing. (b) How long will the boat take to cross the river?

I've done tons of things to try to solve this from pathagreon theorem to sines and cosines and I cannot solve this for the life of me. Please help.

First, figure out the time it would take to cross the river if it was not flowing. Next, consider how far downstream the river would carry the boat in that time. Aim the boat accordingly. (Hint: remember to break the question up into its x- and y-components.)

 

[OlderDan]

I suggest the first step is to find the displacement vector from the starting point to the landing point. The direction of this displacement is the desired direction of the velocity of the boat relative to the ground. You don't have to solve for the angle, but you need the ratio of the components parallel and perpendicular to the current. The velocity relative to the ground is the sum of the river velocity plus the velocity of the boat relative to the river. The components of the boat velocity can be written in terms of the unknown heading of the boat (the speed is given). The components of the resultant velocity can then be written in terms of the heading, and their ratio set equal to the ratio of the displacement components. This will give a solution for the heading, and then the net velocity components can be determined.

 

[rootX]

Can anyone check my answer to this question:

http://img29.picoodle.com/img/img29/9/9/30/f_Untitledm_7fad941.jpg

that's mine solution and here's the book solution

http://img37.picoodle.com/img/img37/9/9/30/f_booksolutiom_ce52c18.jpg

 

[rootX]

they give 37 degree..for the answer

 

[rootX]

oops, I forgot what upstream means, and messed it with downstream