Question

A swimmer heads directly across a river, swimming at her maximum speed of 1.40 m/s relative to the water. She arrives at a point 44.0 m downstream from the point directly across the river, 77.0 m wide. What is the speed of the river current?

Tries 0/8

What is the swimmer's speed relative to the shore?

Tries 0/8

In what direction (as an angle relative to a direct line across the river) should the swimmer aim instead, so that she arrives at the point directly opposite her starting point?

Answer 1

given

v_swimmer = 1.40 m/s
L = 77 m
x = 44.0 m

a)
time taken for the swimmer to cross the river,

t = L/v_swimmer

= 77/1.4

= 55.0 s

speed of the river current, v_river = x/t

= 44/55

= 0.800 m/s <<<<<<<<<----------------Answer

b) The swimmer's speed relative to the shore = distance travelled/timetaken

= sqrt(77^2 + 44^2)/55

= 1.61 m/s <<<<<<<<<----------------Answer

c) let theta is the required angle.

v_swimmer*sin(theta) = v_river

1.4*sin(theta) = 0.8

sin(theta) = 0.8/1.4

theta = sin^-1(0.8/1.4)

= 34.8 degrees <<<<<<<<<----------------Answer