# Question involving trigonometry & river currents

1. Sep 4, 2011

### kiraahhh

1. A man points his rowboat north from A to B, straight across a river of width 100 m. The river flows due east. The man starts across, rowing steadily at 0.75 m/s and reaches the other side of the river at point C, 150 m downstream from his starting point.
What is the speed of the river?

2. Pythagorean Theorem: a^2 + b^2 = c^2

3. 100^2 + 150^2 =
10000 + 22500 = 32500
square rt of 32500 = 180.277

2. Sep 4, 2011

### WatermelonPig

How long does it take him to reach the other side?

3. Sep 4, 2011

### kiraahhh

It doesn't say, but I guess I could do the following:
250 / .75 which is 333.33 seconds.. ?

4. Sep 4, 2011

### PeterO

No - he just rowed straight across the river.

5. Sep 4, 2011

### kiraahhh

So then how do I figure that out? He went across 100 m north then 150 m across, how do I figure out how long it took him? 150 / .75 which is 200 seconds?

6. Sep 4, 2011

### PeterO

He only rowed North, the current took him the 150m East.

Think of an ant walking across a 30cm wide conveyor belt. The ant only walks 30cm, though may end up 100+m from where it started, due to the movement of the conveyor belt.

7. Sep 4, 2011

### kiraahhh

oh! okay yeah so then 200 seconds? right? Or would you take the 180.27 / .75 ?
sorry if I keep dragging this I just want to be sure I got this

8. Sep 4, 2011

### PeterO

Not 200 either - you got theat when you divided 150 by 0.75.

9. Sep 4, 2011

### kiraahhh

so 180.27 / .75 = 240.36?
Am i approaching this correctly?

10. Sep 5, 2011

### PeterO

No!

Come back to the ant on the conveyor belt example.
If the ant crawls at 2 mm/sec, how long does it take to crawl across the 30 cm wide Conveyor belt?
How long would it take to crawl across the conveyor belt if the belt was moving?

The rower is the same.

When the rower is about to start out, he would be able to see the strip of water, 100m long, that he is going to row across, leading to the opposite bank.
If the river was actually a lake, that strip of water would just sit there. But it is a river, and the strip of water [along with the rest of the river] moves down stream at some speed.
He rows across the strip, the strip moves 150m down stream while he rows across his strip of water. At what speed was the strip of water - and the rest of the water in the river - moving downstream?