Chapter 6.3, Problem 33SSC

To determine

The maximum and minimum speed of boat relative to shore.

Answer to Problem 33SSC

The maximum speed of boat relative to shore is $5\text{m/s}$ and minimum speed relative to shore is $0\text{m/s}$ .

Explanation of Solution

Given:

Maximum speed of boat relative to water is $v_{bw}=3\text{m/s}$

Speed of water relative to shore is $v_{ws}=2\text{m/s}$

Formula used:

If velocity of A with repect to B is $V_{AB}$ , velocity of B with respect to C is $V_{BC}$ , then velocity of A with respect to C is

  $V_{AC}=V_{AB}+V_{BC}$

Calculation:

For maximum speed of boat relative to shore, the boat should move with maximum speed in the direction of river flow.

So,

  $\begin{array}{c}{v}_{bs}=v_{bw}+v_{ws}\\ =3+2\\ =5\text{m/s}\end{array}$

For minimum speed of boat relative to shore, the boat should move with same speed of water but in opposite direction.

So,

  $\begin{array}{c}{v}_{bs}=v_{bw}+v_{ws}\\ =\left(-2\right)+2\\ =0\text{m/s}\end{array}$

Conclusion:

Therefore, the maximum speed of boat relative to shore is $5\text{m/s}$ and minimum speed relative to shore is $0\text{m/s}$ .