Physics and Vectors

[BubblegumTroll]

A sailboat is on a southern bank of a river at point (10,0). It needs to get to the dock on the other side at point (35,40). Given that the boat can sail at a speed of 4m/s and the river is flowing east at 5m/s, at what angle must the boat leave the bank to reach the dock in the shortest amount of time. (The angle should be over 90 degrees.)

 

[Deleted member 4993]

A sailboat is on a southern bank of a river at point (10,0). It needs to get to the dock on the other side at point (35,40). Given that the boat can sail at a speed of 4m/s and the river is flowing east at 5m/s, at what angle must the boat leave the bank to reach the dock in the shortest amount of time. (The angle should be over 90 degrees.)

If I were to do your assignment, I would first:

Draw x & y axes and sketch the position of the sailboat.​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[BubblegumTroll]

If I were to do your assignment, I would first:

Draw x & y axes and sketch the position of the sailboat.​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

Based on the question, I have come to 5 equations:
(where x is the boat's velocity along the x-axis; y is the boat's velocity along the x-axis; t is time; theta is what I'm trying to find)

t(x + 5) = 25
t(y) = 40
x^2 + y^2 = 16
x = 4cosθ
y = 4sinθ

I know that x is negative, y is positive, and theta ends up in quadrant 2.

I solved for time and I got an imaginary number. My teacher said I was correct in coming to an imaginary number, but I'm not sure what I'm supposed to conclude finding an imaginary.