Distance of the jetty

Three friends are sitting on a jetty which is exactly in the middle of a flowing river. The first friend sets off against the current of the river at a speed of 0.4 m/s, the second friend sets off along the current of the river at a speed of 0.2 m/s, the third friend swims perpendicularly towards the bank at a speed of 0.8 m/s. The speed of the water flow is 0.5 m/s. Determine the resulting speeds of the first and second swimmers relative to the banks of the river. Determine the resulting speed of the third swimmer relative to the banks of the river, determine what track the third swimmer covers when crossing the river and by what distance the water carries the boat. The width of the entire river is 200 m. The jetty is in the middle. Determine the angle that the vector of the resulting speed of the third swimmer makes with the direction in which this swimmer originally set off (direction perpendicular to the banks of the river).

Final Answer:

v₁ =  -0.1 m/s
v₂ =  0.7 m/s
v₃ =  0.9434 m/s
x =  117.9248 m

Step-by-step explanation:

$$\begin{gathered} p=0.5\text{m/s} \\ a=0.4\text{m/s} \\ b=0.2\text{m/s} \\ c=0.8\text{m/s} \\ {v}_1=a-p=0.4-0.5=-0.1\text{m/s} \end{gathered}$$

$v_2=b+p=0.2+0.5=0.7\text{m/s}$

$v_3=\sqrt{c^2+p^2}=\sqrt{0.8^2+0.5^2}=0.9434\text{m/s}$

$$\begin{gathered} s=200/2=100\text{m} \\ t=s/c=100/0.8=125\text{s} \\ x=v_3\cdot t=0.9434\cdot 125=117.9248\text{m} \end{gathered}$$

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