Respuesta :
Answer:
(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;
[tex]tan(40^{\circ}) = \dfrac{x}{5.75}[/tex]
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
