Question

Suppose a boat moves at 19.0 m/s relative to the water. If the boat is in a river with the current directed east at 1.70 m/s, what is the boat's speed relative to the ground when it is heading east, with the current, and west, against the current? (Enter your answers in m/s.)

Answer 1

Given

Velocity of boat relative to water,

`v_(bw)=19.0\text{ m/s}`

Direction of current towards east,

`v_w=1.70\text{ m/s}`

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?

Step-by-step explanation

When the boat moves along the current,

The velocity of the boat is

`\begin{gathered} v_b=v_(bw)+v_w \\ \Rightarrow v_b=19.0+1.70=20.70\text{ m/s} \end{gathered}`

When the boat travels opposite to the current direction

`\begin{gathered} v_b=v_w-v_(bw) \\ \Rightarrow v_b=1.70-19.0=-17.30\text{ m/s} \end{gathered}`

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.