# Relative velocity of a swimmer

river current = 22 m/s [South]
width of the river from one side to the other = 325m
speed of person swiming = 47 m/s

if the person travels 47 m/s [E 7.5 degrees S] then how far up or down the stream will he end up when he reaches the other side?

alright! i just did a ton of these!

first, find the vector V(current)+V(swimmer)
if you draw it, you get a triange with one leg 47, another 22, and the angle between them 97.5

then solve for the hypotnuse (c^2=a^2+b^2-2ab cos C), which gives you the magnitude of 54.433

use the same equation to get the angle formed by the hypotnuse and the swimmer. this is 23.622 degrees.

since the swimmer is at a 7.5 degree angle, add this to 23.622,
31.122

now you draw the river. from one side to the other is 325 m. now draw a line [E 31.122 S] and use inverse tan to get the answer,
196 m down

someone may want to double check. i might have done something stupid, or even did it wrong all together. haha.

After trying it a few times, I got 196m too..