can someone please help with this:
a.Calculate how long it would take a boat that can travel at 6m/s in still water to cover a distance of 180m down river and back 180m. The water current is 4m/s.
b.The boat is then driven slightly angled against the current so that it travels exactly across the river, whose width is 120m.
Calculate how long it would take the boat to cover the river and back.
I know relative velocity but i never learnt stream questions :/
Hey! So the first one, you just think of it as a constant \(4\) metres per second of velocity, downstream, being added to however fast the boat can travel. So, if it is travelling downstream, it can travel at \(6+4=10\text{ms}^{-1}\). If upstream it is going against the current, so \(6-4=2\text{ms}^{-1}\). So to travel 180m downstream then 180m upstream (in whatever order), we just use the idea that time is distance divided by speed:
The next bit is trickier - The boat driver angles themselves so that they travel directly across the river. What this means is, they make their velocity such a direction that the component of velocity parallel to the stream cancels with the flow of the river, leaving only the horizontal. You'll draw a right angled velocity triangle, with \(4\text{ms}^{-1}\) as the longer arm and \(6\text{ms}^{-1}\) as the hypotenuse (how fast the boat actually travels). Using pythag:
So to cover the 120 metre river:
This might be a little hard to picture without the diagram in front of you - Try to tackle it again having read this and see if it can help you guide your way through