Given
Velocity of boat relative to water,
[tex]v_{bw}=19.0\text{ m/s}[/tex]Direction of current towards east,
[tex]v_w=1.70\text{ m/s}[/tex]To find
What is the boat's speed relative to the ground when it is heading east, with the current, and west, against the current?
Explanation
When the boat moves along the current,
The velocity of the boat is
[tex]\begin{gathered} v_b=v_{bw}+v_w \\ \Rightarrow v_b=19.0+1.70=20.70\text{ m/s} \end{gathered}[/tex]When the boat travels opposite to the current direction
[tex]\begin{gathered} v_b=v_w-v_{bw} \\ \Rightarrow v_b=1.70-19.0=-17.30\text{ m/s} \end{gathered}[/tex]Conclusion
The velocity of boat along the current is 20.70 m/s.
The velocity of boat against the current is -17.30 m/s.
