I wrote it in MIT's 8.01[OCW - Physics] subject, but seems that there are not much movement.. At the end of lecture 12, Prof. Walter Lewin asks if the time for an object that is launched from ground zero with an angle != 0 to reach the maximun altitude (point P) is the same as it to land from there to y=0. Considering air drag. Shall we discuss it?
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At the highest point of altitude what is your velocity?
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I think considering that the drag constant b doesn't change !
http://www.youtube.com/watch?v=9lvNofoUYwI&list=PLF688ECB2FF119649 This is the lecture. The problem is given at the last seconds. Sure the velocity is zero at the highest point, and since we can disconsider the velocity in x axis (?), the only thing that is to be analized is the motion in y axis. I am to say yes, both times are the same, but i wouldn't be surprised if considering drag force could change the asnwer. The viscosity/pressure regime's influency in the motion is quite confuse for me to understand. Moreover, the considered object is a sphere (for simplicity), and just to say, the whole question may have been caused because i'm not so good in english haha. http://ocw.mit.edu//courses/physics/8-01-physics-i-classical-mechanics-fall-1999/lecture-notes/sup5_1.pdf
As the object moves up both g and air drag act downward and hence the retardation is "more" than g. When it comes down g is downwards but air drag is upwards. Hence acceleration is "less" than g. Since vertical distance to be covered is same in both the cases, it will take more time to come down than to go up.