Question

a person rows a boat 8 m/s directly west across a stream that flows south at 6 m/s. what is the resultant velocity of the boat as it crosses the river? a 10 m/s, in a south of west direction b 8 m/s, west c 2 m/s, south d 14 m/s, in a south of west direction

Explanation:

Step1: Identify vector components

The boat's velocity across the stream is $v_x = 8$ m/s (west - direction) and the stream's velocity is $v_y=6$ m/s (south - direction). These are two perpendicular vector components.

Step2: Use Pythagorean theorem for magnitude

The magnitude of the resultant velocity $v$ is given by $v=\sqrt{v_x^{2}+v_y^{2}}$. Substitute $v_x = 8$ m/s and $v_y = 6$ m/s into the formula: $v=\sqrt{8^{2}+6^{2}}=\sqrt{64 + 36}=\sqrt{100}=10$ m/s.

Step3: Determine direction

Since the two velocities are perpendicular (west and south), the resultant velocity is in the south - of - west direction.

Answer:

A. 10 m/s, in a South of West direction