# Math Help - Finding Width Of A River

1. ## Finding Width Of A River

Not sure if this is the right forum for this, but this was a question assigned in my calculus class. And I'm pretty sure you can use calculus to solve it.

Find the width of a river if you are using a 10cm ruler.

A couple of things to consider are:

Similar triangles (I'm not sure what he means by those... maybe the special triangles?)

and

Environment

Any help is appreciated.

2. ## Finding the width of a river

Hello Shapeshift
Originally Posted by Shapeshift
Not sure if this is the right forum for this, but this was a question assigned in my calculus class. And I'm pretty sure you can use calculus to solve it.

Find the width of a river if you are using a 10cm ruler.

A couple of things to consider are:

Similar triangles (I'm not sure what he means by those... maybe the special triangles?)

and

Environment

Any help is appreciated.
I don't have any suggestions that involve calculus, but I do have some that use similar triangles. (And I'm assuming that you can cross the river, and that 'Environment' includes things like trees, buildings, and other random bits of stuff.)

1 Find a 'random bit of stuff' about, say, 2 m in length; e.g. a piece of wood, a willing friend, etc.

2 Measure its length carefully with the 10 cm ruler.

3 Find a tree, tall building, etc near the bank of the river on the side which you currently are on.

4 Lie on the ground so that your eye is just above ground level. Mark on the ground the position of your eye.

5 Position the 'random bit of stuff' in such a way that its height appears to be the same height as the tree (building, etc.)

6 Use the ruler to measure the distance between the position of your eye and the foot of the 'bit of stuff'.

7 Use the bit of stuff to measure the distance between the position of your eye and the foot of the tree.

8 Use similar triangles to calculate the height of the tree.

9 Cross the river and position yourself on the bank directly opposite the tree.

10 Repeat steps 4 to 6.

11 Knowing the distance of your eye from the 'bit of stuff', the height of the tree and the height of the 'bit of stuff', use similar triangles to calculate the width of the river.

3. Hello, Shapeshift!

(1) Use the ruler to measure the bridge
. . .which is just a half-mile downstream.

(2) Stick the ruler in the bank on one side of the river.
. . .From the opposite bank, fire a rifle at the ruler,
. . .carefully measuring the time from the shot
. . .to the sound of the ruler breaking.
. . .Knowing the muzzle velocity of your rifle
. . .and the speed of sound for your altitude,
. . .you can calculate the width of the river.

(3) Go to the local geography expert and say,
. . ."If you don't tell me the width of that river,
. . .I will hit you with this 10-cm ruler."

4. ## Now why didn't I think of that...

Originally Posted by Soroban
Hello, Shapeshift!

(1) Use the ruler to measure the bridge
. . .which is just a half-mile downstream.

(2) Stick the ruler in the bank on one side of the river.
. . .From the opposite bank, fire a rifle at the ruler,
. . .carefully measuring the time from the shot
. . .to the sound of the ruler breaking.
. . .Knowing the muzzle velocity of your rifle
. . .and the speed of sound for your altitude,
. . .you can calculate the width of the river.

(3) Go to the local geography expert and say,
. . ."If you don't tell me the width of that river,
. . .I will hit you with this 10-cm ruler."