# What angle should a swimmer aim to land directly across the starting position?

• WorkingHard2017
In summary: The swimmer's velocity relative to the water is on the hypotenuse, and the current is on the other two sides.
WorkingHard2017

## Homework Statement

A swimmer who achieves a speed of of 0.75 m/s in still water swims directly across a river 72m wide. The swimmer lands on the far shore at a position 54m downstream from the starting point. Determine the direction the swimmer would have the aim to land directly across from the starting position

## Homework Equations

v swimmer relative to ground = v swimmer relative to water + v water relative to ground

## The Attempt at a Solution

v water relative to ground = 0.56 m/s[/B]
tanθ = (0.56/0.75)
θ = 37° downstream from the starting position

so to land directly across the starting point, the swimmer would need to aim 37° upstream from the starting position. Is this correct? My book says 42° upstream from the starting position, but I can't see how that makes sense.

WorkingHard2017 said:
water relative to ground = 0.56 m/s
Actually, you do not need to know any speeds. The two distances are enough information.
(I'm getting 49 degrees.)

Last edited:
I wonder if the book is considering the angle to be between the shoreline and the swimmer's trajectory?

gneill said:
I wonder if the book is considering the angle to be between the shoreline and the swimmer's trajectory?
That's probably the explanation, though for that I make it much closer to 41 degrees.

Hi there, so to get 0.56 m/s, I determined that since the swimmer travels 0.75 m/s, he would travel 72m in 96s. From there, I divided the length of the river, (54m) by 96s to get a speed of 0.56m/s.

gneill said:
I wonder if the book is considering the angle to be between the shoreline and the swimmer's trajectory?
haruspex said:
That's probably the explanation, though for that I make it much closer to 41 degrees.

WorkingHard2017 said:
Hi there, so to get 0.56 m/s, I determined that since the swimmer travels 0.75 m/s, he would travel 72m in 96s. From there, I divided the length of the river, (54m) by 96s to get a speed of 0.56m/s.
Ok. Your error is in assuming that the angle that the swimmer gets carried downstream when swimming straight across relative to the water is the same as the angle the swimmer has to aim upstream. E.g. when aiming upstream the time taken to cross increases, so the current gets to carry the swimmer further.
Draw the right-angled vector triangle for the swimming upstream case. Which side represents the swimmer's velocity relative to the water and which side the current?

## 1. What is relative velocity?

Relative velocity is the measurement of the velocity of an object in relation to another object. It takes into account the motion of both objects and is usually measured in terms of speed and direction.

## 2. How is relative velocity calculated?

Relative velocity can be calculated using vector addition. The velocity of the first object is added to the velocity of the second object, taking into account their direction and speed. The resulting vector is the relative velocity between the two objects.

## 3. What is the difference between relative velocity and absolute velocity?

Absolute velocity is the velocity of an object in relation to a fixed reference point, while relative velocity is the velocity of an object in relation to another moving object. Absolute velocity is constant, while relative velocity can change depending on the motion of both objects.

## 4. How does relative velocity affect collisions?

Relative velocity plays a crucial role in collisions between objects. It determines the direction and speed of the objects after the collision and can help predict the outcome of the collision. Objects with higher relative velocities will have more forceful collisions.

## 5. Can relative velocity be negative?

Yes, relative velocity can be negative. This occurs when the two objects are moving in opposite directions, resulting in a negative value for the relative velocity. However, the negative sign only indicates the direction of the relative velocity, not the actual speed.

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