Perpendicular direction

A speedboat moves relative to the water at a constant speed of 13 m/s. The speed of the water current in the river is 5 m/s

a) At what angle concerning the water current must the boat sail to keep moving perpendicular to the banks of the river?
b) At what speed does the boat approach the opposite bank?

Correct answer:

α =  112.6199 °
v₃ =  12 m/s

Step-by-step explanation:

$$\begin{gathered} v_1=13\text{m/s} \\ {v}_2=5\text{m/s} \\ \cos \beta =v_2/v_1 \\ \beta =\frac{180°}{\pi }\cdot \arccos (v_2/v_1)=\frac{180°}{\pi }\cdot \arccos (5/13)\doteq 67.3801{}^{\circ } \\ \alpha =180-\beta =180-67.3801=112.6199^{\circ }=112°37^{\prime }11" \end{gathered}$$

$v_3=v_1\cdot \sin \beta =v_1\cdot \sin 67.38013505196°=13\cdot \sin 67.38013505196°=13\cdot 0.923077=12=12\text{m/s}$

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