A swimmer heads directly across a river, swimming at 1.2 m/s relative to the water. She arrives at a point 48 m downstream from the point directly across the river, which is 77 m wide.

Question

A swimmer heads directly across a river, swimming at 1.2 m/s relative to the water. She arrives at a point 48 m downstream from the point directly across the river, which is 77 m wide.
(a) What is the speed of the river current?

(b) What is the swimmer's speed relative to the shore?

(c) In what direction should the swimmer head so as to arrive at the point directly opposite her starting point?

Henry · Answer

a. Tan A = 48/77 = 0.62338
A = 31.94o

Tan31.94 = Vc/1.2
Vc = 1.2*Tan31.94 = 0.748 m/s = Speed of
the current.

b. Vs = 1.2/Cos31.94 = 1.414 m/s = Speed of swimmer.

c. The current shifted the swimmer 31.94o E. of the desired point. To offset the affect of the current, the
swimmer must head 31.94o west of the
desired point.