Question

A boat is moving due east at 15 miles per hour when it encounters a current LaTeX: \textbf{C} = 2\textbf{i}+17\textbf{j}C = 2 i + 17 j. What is the path of the boat in this current if the boater keeps it pointed due east? What direction should the boater steer in order to go due east?

Answer 1

Answer:

a) $\vec v_{B} - \vec v_{C} = 3\, i - 17\,j$, b) $\theta = 79.992^{\textdegree}$ (clockwise)

Step-by-step explanation:

The resultant velocity of the boat must be:

$\vec v_{B} = 15\,i$

Likewise, the velocity of the current is:

$\vec v_{C} = 2\,i + 17\,j$

a) The intended velocity of the boat is:

$\vec v_{B} - \vec v_{C} = (15-2)\,i + (0-17)\,j$

$\vec v_{B} - \vec v_{C} = 3\, i - 17\,j$

b) The direction of the boat is:

$\theta = \tan^{-1}\left(\frac{17}{3} \right)$ (clockwise)

$\theta = 79.992^{\textdegree}$ (clockwise)