Question: A swimmer has a swimming speed of 5.75 m/s in still water. When she heads directly across the river, she ends up travelling downstream at an angle of 40°
(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 river is 15 m wide, how long would a trip directly across the river take?

(a) 4.82 m/s

(b) The simmer need to head 57.05° upstream of the river to reach a point directly opposite the river

(c) 4.024 seconds

Explanation:

The parameters given are;

The speed of the swimmer = 5.75 m/s

The direction of the resultant motion = 40° downstream

The speed of the current = x m/s

Therefore in a given second, we have that the swimmer moves 5.75 meters across the river while the current moves x meters downstream

Which gives;

x = 5.75 × tan(40°) = 4.82 m/s

The speed of the current = 4.82 m/s

(b) If the swimmer swims at a direction θ to reach a point, p, directly opposite the river, we have;

The resultant speed across the river will be the swimmer's swimming speed which is 5.75 m/s

5.75² = y² + 4.82²

y = √(5.75² - 4.82²) = √9.78

tan(θ) = 4.82/(√9.78) = 1.54

θ = tan⁻¹(1.54) = 57.05°

The simmer need to swim 57.05° upstream to reach a point directly opposite the river

(c) If the river is 15 m wide, we have;

Time (t) = Distance/speed

The component of the swimmer's speed directly across the river = 5.75/(tan(57.05°)

The component of the swimmer's speed directly across the river = 3.73 m/s

The time, t, to cross the river is therefore;

t = 15/3.73 = 4.024 seconds

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.