<p>Dave rows a boat across a river at 4.0 m/s. The river flows at 6.0 m/s and is 360 m across.<br>
a. In what direction, relative to the shore, does Dave's boat go?
b. How long does it take Dave to cross the river?
c. How far downstream is Dave's landing point?
d. How long would it take Dave to cross the river if there were no current?</p>
<p>(a) Dave travels in a vertical direction, the river travels in a horizontal direction. Relative to the shore, he will be traveling with a velocity equal to the sum of the two velocity vectors, which if you use tip-to-tail method, would be a hypotenuse of a right triangle, so it's just sqrt(16+36)m/s. For the angle, it's the arctan(4/6). Use arctan(y/x) to get this</p>
<p>(b) Since the river's motion is perpendicular to Dave's motion, it doesn't have any effect on the time it takes Dave to cross the river, so it's just 360/4=90s</p>
<p>(b) wait, I read that wrong, that's the answer for d. for b just use the answer you found in a and divide 360 by that</p>
<p>and for c use the answer you got in b and multiply it by the horizontal component, which is 6m/s to get the answer</p>
<p>You know what? Thinking about it, stick with the previous statement about b, because Dave still has a vertical component of 4m/s regardless of the river's motion, since both are perpendicular, so the answer to both b and d is 90s. The only difference when there is current is that Dave will end up somewhere downstream while as with no current he won't</p>
<p>Thank you so much for taking your time to answer these questions!</p>
<p>I am no physics expert, but wouldn't the answer to part b be larger than the answer to part d? The shortest distance between two parallel lines (the banks of the river) is the line which is perpendicular to both of the lines. Thus, if there is a force which pushes Dave down the river, as stated below, then he travels at an angle of arctan(4/6). This is a longer distance.</p>
<p>I think that the final distance he travels is arctan(4/6)=cos(360/distance)
I'd say the answer to part b is then (4.0 m/s)/distance)</p>
<p>The only problem is that I don't know if 4.0 m/s is a one axis component, or the speed it takes him to cross the river at any angle.</p>
<p>But then again, I could be speaking only rubbish :)</p>
<p>It is a one axis component. The 360 m distance is in the y-direction and so is the velocity of the river. The flow of the river is in the x-direction and thus perpendicular to the distance across the river</p>
<p>I think the real question that you're trying to drive at is, is Dave's speed of 4 m/s a distance traveling strictly vertically between the two banks, or is Dave's speed of 4 m/s a distance traveling diagonally along the hypotenuse of his travel vector?</p>
<p>Considering the phrasing of the question that "Dave rows a boat across a river at 4 m/s", I'd interpret this as the former. I would say that the statement of "Dave is rowing a boat that is traveling at 4 m/s" implies more of the latter.</p>
<p>That's just my thought there.</p>