# Calculating Swimmer's Distance and Time Across River Q

• Naeem
In summary, a river 590 ft wide flows with a speed of 6 ft/s with respect to the earth. A woman swims with a speed of 3 ft/s with respect to the water. If the woman heads directly across the river, how far downstream is she swept when she reaches the opposite bank? If she heads 29° upstream, how far downstream is she swept before reaching the opposite bank? For the conditions of part b, how long does it take for her to reach the opposite bank? For the conditions of part c, how long does it take for her to reach the other side?
Naeem
Q. A river 590 ft wide flows with a speed of 6 ft/s with respect to the earth. A woman swims with a speed of 3 ft/s with respect to the water.
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a) If the woman heads directly across the river, how far downstream is she swept when she reaches the opposite bank?
d1 = ft *
1179.96 OK

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b) If she wants to be swept a smaller distance downstream, she heads a bit upstream. If she heads 29° upstream, how far downstream is she swept before reaching the opposite bank?
d2 = ft

Any ideas on part b

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c) For the conditions of part (b), how long does it take for her to reach the opposite bank?
Any ideas on part c

Aha I remember this from vectors in grade 10.

Remember relative velocity law:

V woman,earth = V woman,water + V water,earth

Draw your diagrams, look at the components, add them. find scalar multiple k so that the vertical component is 590 (the width of river) and the horizontal component is how far she is swept downstream. k is the time it takes to get the the other side.

Part b: exactly the same as part a, except change your vectors so she heads 29 degrees instead of being perpendicular to the current of the river.

Part c: same as part a; find k a scalar multiple such that the vertical component is the width of the river. k is the time it takes.

By the way it's so funny seeing things in feet and feet per second. I kind of gained an impression about how annoying it must be for poor americans learning science and having been brought up to know the old-fashioned units and not metric!

Here is what I did for part b,

d = v0 cos theta * t

width of the river, d = 590 m

velocity of the river = 6ft /s

velocity of the woman = 3ft/s

so, t = d / vwoman * cos (29)

t= 590 /3 * cos(29)

After finding t , we can multiply this t with 6 ,which is the velocity of the river.

No luck with this problem for the last 2 parts, can anybody tell me if something is wrong here.

## 1. How do you calculate a swimmer's distance across a river?

To calculate a swimmer's distance across a river, you would use the Pythagorean theorem. This involves measuring the width of the river, the angle of the swimmer's path, and the speed of the current. Using these measurements, you can calculate the distance using the formula: Distance = Width * sin(Angle) / sin(90° - Angle).

## 2. How do you calculate a swimmer's time across a river?

To calculate a swimmer's time across a river, you would use the formula: Time = Distance / Speed. This involves knowing the distance across the river and the swimmer's speed in the water. If there is a current, the swimmer's speed would be their swimming speed minus the speed of the current.

## 3. How does the current affect a swimmer's distance and time across a river?

The current can have a significant impact on a swimmer's distance and time across a river. If the current is moving in the same direction as the swimmer, it can decrease the distance and time. However, if the current is moving in the opposite direction, it can increase the distance and time. It's important to factor in the speed and direction of the current when calculating a swimmer's distance and time across a river.

## 4. What is the best way to measure a swimmer's path across a river?

The best way to measure a swimmer's path across a river is to use a protractor or angle finder to measure the angle of the swimmer's path. This will give you the most accurate measurement and allow you to calculate the distance more precisely using the Pythagorean theorem.

## 5. Are there any other factors to consider when calculating a swimmer's distance and time across a river?

Yes, there are a few other factors to consider when calculating a swimmer's distance and time across a river. These include the swimmer's physical abilities, the water conditions (such as waves or temperature), and any potential obstacles in the river. These factors can affect the swimmer's speed and should be taken into account when making calculations.

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