<p>Yeah...sorry megamike, I wasn't really thinking when I wrote that. The top of its trajectory is when v=o and since 0=vo-at, when a is greater, then t would be smaller, thereby making it take less time to rise and more time to fall. The particle must overcome more resistance to ascent when it is rising, but it falls much more freely during its decent.</p>
<p>potpurri, going down does take longer. The test did ask for justification, and I certainly did not include proof by contradiction in my answer. However, although the answer pretty much has to be based on intuition, I was trying to make it clear in an extremely rigorous way - thus my rambling up above.</p>
<p>"The ball falls faster on the way down bc Fg works to accelerate in downward direction, wheras this decelerates motion in the upward direction."</p>
<p>Think about your reasoning for a second. Did you even use the fact that there is air resistance? If this was a valid justification, it would apply even if the air wasn't there, which can't be possible, since without resistance the time it takes the ball to rise and descend will be the same.</p>
<p>I got the same DE as ohnoes. I'm pretty sure the current graph did not approach zero, though I'm also pretty sure I failed that problem, so I might not be the best person to believe there ;)</p>
<p>And the ball definitely took longer coming down.</p>
<p>i got that it started out as vo and approached zero like...inverse parabolic? and then when it hit zero at the 1/2 point it did the same thing again inverse parabolic (i mean the shape was like that not the actual equation) until Vt</p>
<p>Rilla- that's exactly what I got. hopefully we both got it :) I'm pretty sure both the ends should be the same, but I didn't know what happened in the middle so I just randomly drew a parabolic shape.</p>
<p>Hey guys, for the diff. eq., does it matter if you isolated the derivative?</p>
<p>Also, when they asked for the diff. eq. is g negative? In the table of constants, g is 9.8 m/s^2 at the earth's surface so I put something to the effect of dv/dt=-g-kv/m </p>
<p>I'm pretty sure it can be negative. If the scoring guidelines for past FRQ's are any indication, it really doesn't matter whether or not you isolated the derivative to get creadit.</p>