Re: Which one will take less time to land if the air friction is proportional t

Matthew:

May I assume that you are working a classical problem with some odd specific parameters? Part 
of the odd nature of this question is the linear relationship between the speed and what you call 
air friction. Wind resistance (air friction) is normally considered to increase with the square of the 
velocity; but IÕm not sure that this will change your results in this question. Another odd part of 
your question is that the mass and the proportionality factor to calculate the effect of the air are 
not given. You must be able to use any braking acceleration you want for this question. I would 
suggest something like 1 m/s/s for each 10 m/s of speed. Finally, there is the five significant 
digit height of the building compared to the two significant digit horizontal velocity. This would 
indicate that precision is not going to play a large factor in your answer. IÕll also assume that you 
are not expected to use any numeric procedures to work this problem or to let a spreadsheet do 
the work. In addition, you might be using the acceleration of gravity as 10, 9.8, or 9.81 m/s/s.

My suggestion is to pick proper viewing points. Avoid the side view where you would see an arc 
curving down. Rather pick two views to single out either the vertical motion or the horizontal 
motion. For the two drops, that will require four sets of calculations. To clearly see only the 
vertical drops, picture yourself far away and looking toward the building along the plane of the 
initial horizontal shot. The object will be coming toward you but you would only see it moving 
downward. For the other view, consider yourself high up and looking down at the drop. Now the 
horizontal motion would be obvious while the vertical drop would not.

Your job is to calculate the position of the object after each second in both the horizontal and 
vertical direction. If you do this for the first 3-4 seconds, you will see how the horizontal push 
affects the vertical motion and can predict the effect in reaching the bottom either sooner or 
later.

Good luck,
Gene Ewald