Short method:
Assuming the direction that she is swimming is directly across the river (y-direction), and she is swept downstream (x-direction) by the current in the river. We can directly calculate her y-velocity:
y = v*t
v = y/t = 200/(6*60 + 40) = 0.5 m/s
Long method:
The river’s speed does not contribute to her progress across the river. It only provides an x-direction component. If we want to calculate her component of velocity over the resultant path, we would calculate the resultant distance and velocity.
v_x = 480m/400s = 1.2 m/s
v_x is the speed of the river current
The distance covered is calculated using hypotenuse formula:
d = sqrt(200^2 + 480^2) = 520 m
The resultant velocity is:
v = d/t = 520/400 = 1.3 m/s
However this is still the resultant speed of the swimmer and the river current together. Therefore using the hypotenuse formula again to find for v_x:
v^2 = v_x)^2 + (v_y)^2
v^2 - (v_x)^2 = (v_x)^2
v_y = sqrt [ v^2 - (v_x)^2 ] = sqrt( 1.3^2 - 1.2^2) = 0.5 m/s
This is the swimmers velocity without the current.
Answer:
0.5 m/s
