Question

A river flows due south with a speed of 1.4 m/s . you steer a motorboat across the river; your velocity relative to the water is 4.7 m/s due east. the river is 660 m wide. part a what is the magnitude of your velocity relative to the earth? express your answer with the appropriate units.

Answer 1

Refer to the diagram shown below.

The river flow south at a velocity of 1.4 m/s.
The motorboat moves east with velocity of 4.7 /s

The velocity of the motorboat relative to the earth, v, is the vector sum of the two velocities. Its magnitude, by the Pythagorean theorem, is
v = √(4.4² + 1.4²)
= 4.904 m/s

Its direction south of east, is at an angle, θ, given by
tan θ = 1.4/4.7 = 0.298
θ = tan⁻¹ 0.298 = 16.6°

Answer:
The velocity of the motorboat is 4.9 m/s, at 16.6° south of east.