Question

A boat is moving at 30 kph in crossing a river in which the current is flowing at 12 kph.In what direction should the boat head if it is to reach a point on the other side of the river directly opposite its starting point.check your answer with a graphical solution.

Answer 1

Answer on Question #45832, Physics, Mechanics | Kinematics | Dynamics

Task: A boat is moving at $30\mathrm{km / h}$ in crossing a river in which the current is flowing at $12\mathrm{km / h}$ . In what direction should the boat head if it is to reach a point on the other side of the river directly opposite its starting point. Check your answer with a graphical solution.

Answer:

$$\begin{array}{l} \overline {{V _ {b}}} = 3 0 k m / h; \\ \overline {{V _ {r}}} = 1 2 k m / h; \\ \end{array}$$

The resultant speed is the hypotenuse: $\sqrt{30^2 + 12^2} = \sqrt{1044} \approx 32.31$

but the boat is moving at an angle relative to the perpendicular-line that connects two points on opposite banks, because the current will always reject at a small angle to the direction of flow. Let the angle is $\alpha$ , so $\tan \alpha = \frac{12}{30} \Rightarrow \alpha = \arctan \frac{6}{15}$

therefore the boat is moving at an angle $\alpha = \arctan \frac{6}{15}$ against the direction of traffic flow.

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