Question

A person can swim 0.65 m/s in still water. She heads directly south across a river 130 m wide and lands at a point 88 m [W] downstream.

a)determine the velocity of the water relative to the ground.
b)the swimmer's velocity relative to Earth.
c) the direction she should swim to land at a point directly south of the starting point.

Answer 1

we know that that the person traveled a distance of

sqare root**[(30^2) + (80^2)] = 85.44m

We know that that his velocity up stream is 0.65 m/s so we can find the time.
130m/0.65m/s = 200 seconds. To find the velocity of the current we can do this.

88m = Vcurrent(t) so the velocity of the current is = 88m/200m = 0.44 m/s downstream.

The swimmers velocity is the addition of the current and his own velocity up stream.

Vo = square root **[(0.65)^2 + (0.44)^2] = 0.78 m/s to find the angle do

arctan(0.65m/s/-0.44 m/s) = -55.9 degrees ----- 180 + (-55.9) = 124.09 degrees. You can say its 0.78 m/s [ N 34.09 degrees W)


SO for this one we have a current against us so we have to swim at an angle.


Because this person wants to go straight down steam his horizontal component must equal zero. so 0.44 = 0.65costheta.. the angle must be 47.4 degrees..

Double check my work alright. I think this is it.