Chapter 15, Problem 1IP

Summary Introduction

To determine: The velocities of the swimmer with respect to the current when the boy swims directly upstream and directly downstream.

Answer to Problem 1IP

The velocities of the swimmer with respect to the current when the boy swims directly upstream and directly downstream are 2 m/s in the upstream and 1 m/s in the downstream.

Explanation of Solution

Calculation:

The velocity of the swimmer with respect to the current when the boy swims directly upstream is,

$v_{\text{b/c}}=v_{\text{b}}+v_{\text{c}}$

Here, $v_{\text{b/c}}$ is velocity of the swimmer with respect to the current when the boy swims directly upstream, $v_{\text{b}}$ is velocity of the boy, and $v_{\text{c}}$ is velocity of the current.

Substitute $1.5\text{m/s}$ for $v_{\text{b}}$ and 0.5 m/s for $v_{\text{c}}$ to find $v_{\text{b/c}}$.

$\begin{array}{c}{v}_{\text{b/c}}=1.5\text{m/s}+0.5\text{m/s}\\ =\text{2 m/s}\end{array}$

Thus, the velocity of the swimmer with respect to the current when the boy swims directly upstream is 2 m/s.

The velocity of the swimmer with respect to the current when the boy swims directly downstream is,

$v_{\text{b/c}}=v_{\text{b}}-v_{\text{c}}$

Here, $v_{\text{b/c}}$ is velocity of the swimmer with respect to the current when the boy swims directly downstream, $v_{\text{b}}$ is velocity of the boy, and $v_{\text{c}}$ is velocity of the current.

Substitute $1.5\text{m/s}$ for $v_{\text{b}}$ and 0.5 m/s for $v_{\text{c}}$ to find $v_{\text{b/c}}$.

$\begin{array}{c}{v}_{\text{b/c}}=1.5\text{m/s}-0.5\text{m/s}\\ =1\text{ m/s}\end{array}$

Thus, the velocity of the swimmer with respect to the current when the boy swims directly downstream is 2 m/s.

Conclusion

Therefore, the velocities of the swimmer with respect to the current when the boy swims directly upstream and directly downstream are 2 m/s in the upstream and 1 m/s in the downstream.