# What is the velocity of the boat relative to the water

1. Mar 6, 2005

### carltonblues

Bernie is showing Margaret his new boat and its auto-navigation feature, of
which he is particularly proud. "The island is 1 km east and 3 km north of this
dock. So I just punch the numbers like this, and we get ourselves refreshment
and enjoy the scenery." 45 min later, they find themselves due east of the
island. "OK, something went wrong. I just reverse the instructions, and we'll go
back to the dock and try again." But 45 min later the boat is 6 km east of their
original position at the dock. "Did you allow for the current?" asks Margaret.
"For what?" says Bernie.
1) What is the velocity of the current in the waterway where Margaret and
Bernie are boating?
2) What is the velocity of the boat relative to the water, for the first 45 min?
3) What is the velocity of the boat relative to the island for the first 45 min?

It seems easy at first, but the current is giving me trouble. I used pythagoras to find the distance of 3.16km to the island if there was no current but am having trouble calculating the current out of that. Please help!

2. Mar 6, 2005

### Astronuc

Staff Emeritus
Take the dock as the origin (0,0). If the boat is due east after 45 min (0.75 hr), then there must be a current which has an average velocity of 3 km/0.75 hr = (4 km/hr) in the southerly direction. But the problem does not state how far east they are after 45 minutes (this is another unknown).

But then after another 45 minutes, they are still east ( but it does not say 'due' east), but now 6 km out, after reversing the boats velocity.

3. Mar 6, 2005

### carltonblues

If the current is in the sotherly direction, then why does the boat go off course so much when they reverse the co-ordinates?

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