Question

a swimmer can swim in still water at a speed of 9.50 m/s. he intends to swim directly across the river that has a downstream current of 3.75 m/s. what is his velocity relative to the bank?

Answer 1

Refer to the diagram shown below.

Still-water speed  = 9.5 m/s
River speed = 3.75 m/s down stream.

The velocity of the swimmer relative to the bank is the vector sum of his still-water speed and the speed of the river.

The velocity relative to the bank is
V = √(9.5² + 3.75²) = 10.21 m/s

The downstream angle is
θ = tan⁻¹ 3.75/9.5 = 21.5°

Answer:  10.2 m/s at 21.5° downstream.

Answer 2

The relative velocity of swimmer to the bank is $\boxed{10.21\text{ m/s}}$ and $\boxed{21.54^\circ}$ downstream.

Further Explanation:

The swimmer swims across the river from one end to the other. The river is flowing downstream.

The swimmer will cross the river with some relative velocity.

Given:

The velocity of swimmer is $9.50\text{ m/s}$.

The velocity of river is $3.75\text{ m/s}$ downstream.

Concept:

Consider the direction of velocity of swimmer in positive x-direction.

The velocity of swimmer in vector form:

$V_s=9.50\hat i$

Consider the direction of downstream current of river in negative y-direction.

The velocity of downstream current in vector form:

$V_r=- 3.75\hat j$  

The relative velocity of swimmer to the bank is the resultant of two vectors in x and y direction.

Magnitude of relative velocity:

${V_{sr}}=\sqrt{V_r^2+V_s^2}$  

Substitute $9.50\text{ m/s}$ for $V_s$ and $3.75\text{ m/s}$ for $V_r$ in above equation.

$\begin{aligned}{V_{sr}}&=\sqrt{3.75^2+9.50^2}\text{ m/s}\\&=10.21\text{ m/s}\end{aligned}$

The magnitude of relative velocity of swimmer is $10.21\text{ m/s}$ .  

The direction of relative velocity:

$\theta={\tan^{-1}}\left({\dfrac{{{V_r}}}{{{V_s}}}}\right)$  

Substitute $9.50\text{ m/s}$ for $V_s$ and $-3.75\text{ m/s}$ for $V_r$ in above equation.

$\begin{aligned}\theta&={\tan^{-1}}\left({\dfrac{{{-3.75}}}{{{9.50}}}}\right)\\&=21.54^\circ\end{aligned}$

The direction of relative velocity is $21.54^\circ$ downstream.

Thus, the relative velocity of swimmer to the bank is $\boxed{10.21\text{ m/s}}$ and $\boxed{21.54^\circ}$ downstream.

Learn more:

1. Volume of gas after expansion: https://brainly.com/question/9979757

2. Principle of conservation of momentum: https://brainly.com/question/9484203

3. Average translational kinetic energy: https://brainly.com/question/9078768

Answer Details:

Grade: Middle School

Subject: Physics

Chapter: Scalars and vectors

Keywords:

Swimmer, still, water, speed, 9.50 m/s, intends, directly, river, downstream, current, 3.75 m/s, velocity, relative, bank, vector, direction, 21.5degree and 10.21 m/s.