River crossing physics problem

Question

A swimmer has a swimming speed of 5.2 m/s in still water. When she heads directly across the river, she ends up travelling downstream at an angle of 30° (with respect to a line perpendicular to the shore).  

       

(a)   What is the speed of the current?

(b)   What heading would the swimmer need to have in order to reach a point directly across the river?

(c)   If the stream is 15 m wide, how long would a trip directly across the river take?

Answer 1

The velocity added with current speed, let it be V.

Vcos30 = 5.2 m/s ( vertical )

Vsin30 = V_current (horizontal)

V x (√3)/2 = 5.2 Then V = 10.4/√3 = 6 m/s

V_current = 6 x 0.5 = 3 m/s

b) The swimmer should swim with 30 opposite heading to the current so that his/her horizontal component cancels out the current velocity and reaches directly across.

c) Crossing time is determined by the vertical velocity while the horizontal component determines the distance from the directly-across point of arrival.

So

d = V(vertical) x t

15 = 5.2 x t

t = 2.9s