Question

Suppose a river flows south to north at a velocity of 1 m/s, and a motorboat traverses the river from east to west at a speed of 2.5 m/s. At what angle should the boat be oriented south, relative to the westward direction, such that the boat will be traveling due west? Round to the nearest degree.

Answer 1

Answer: $24^{\circ}$

Step-by-step explanation:

Given

River is flowing from south to North with a velocity of $u=1\ m/s$

Motor boat traverses the river from east to west at a speed of $v=2.5\ m/s$

South component of boat velocity must compensate the river velocity in order to travel in west direction.

$\therefore v\sin \theta=u\\\\\Rightarrow 2.5\sin \theta=1\\\\\Rightarrow \sin \theta=\dfrac{2}{5}\\\\\Rightarrow \theta=23.57^{\circ}\approx 24^{\circ} \text{south of west}$