[babi_gurl]

Hey I got a question that I am stuck with and need some help on it
A boat that is capable of travelling at 4.5km/hr in still water is travelling on a river whose current is 1.5jm/h East.
Find the time it takes for the boat to travel 3.0km downstream relative to the shore. And
The time the boat takes to travel 3.0 km upstream against the current

Thanks

[Capuchin]

Okay well all you do is add the vectors!

Lets say that the direction of motion in the same direction as the current is positive.

In the first case, travelling downstream, the velocity is 4.5km/hr for the boat and 1.5km/hr for the current, these are both positive because they are both in the same direction as the current, like we defined above, this adds to give 6km/hr total velocity. Now you can work out the time taken in this case.

In the second case, the boat's speed is -4.5km/hr (4.5km/hr in the direction opposite to the current's direction, this is why it is negative) and the current's speed is 1.5km/hr (positive because it is in the direction of the current). These add to give a velocity of -3km/hr, so this is 3km/hr upstream. Now you can work out the time this takes to go upstream.

I hope this helped you to understand the basics of vector addition. And helps you to see how useful vectors are for forces in different directions.
When we define the motion in one direction as positive at the beginning, it doesn't matter which direction we choose, I could have chosen the current's direction as negative, and got different answers, but the answers would have the same meaning if you refer back to the same defined system. Normally you choose the system to be easier to interpret in your mind.