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)`

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=(2)/(5)\\\\\Rightarrow \theta=23.57^(\circ)\approx 24^(\circ) \text{south of west}`