Physics- Velocity w/ respect to Observer?

Question

The boat in Figure 3.17 is heading due north a it crosses a wide river with a velocity of 10.0 km/h relative to the water. The river has a uniform velocity of 5.00 km/h due east. Determine the velocity of the boat with respect to an observer on the riverbank.

Please explain clearly with steps...

Answer 1

The boat's velocity has two components: North 10 and East 5. Start by determining the scalar speed, using the Pythagorean theorem:

s² = 10² + 5²

s² = 125

s = 11.18 km/hr

To determine the velocity, we need to know the direction as well as the speed. For that, we find the angle whose tangent is 5 / 10.

φ = arctan(5 /10)

φ = arctan(.5)

φ = 26.6°

So the boat's v is 11.18 km/hr at 26.6° east of north.