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| Please ignore the glow-in-the-dark dinosaurs. Thank you. |
As you can see, my door is a rather dull dark brown. I try to liven it up with some decorations. (If it looks pitiful, that's because I'm in the middle of changing over the posters and stuff.) I found this really spiffy water color painting a while back, and decided to put it up. That's all well and good, except that the door is solid wood, and my parents might take badly to me putting things up using thumbtacks and a really big hammer. Instead, I've been using blue poster tack.
However, it isn't as sticky as I'd like, and sometimes the corners come unstuck, as you can see. When that happens, it's only a matter of time until the painting falls off entirely. Sod's Law (also called Murphy's Law) dictates that it will do so just as I'm attempting something that requires great delicacy and precision.
If we ignore wind resistance and assume the poster falls with the same orientation as above (instead of, say, turning over a few times), we can calculate the time it takes to hit the ground and the velocity it has when it does so.
Lesse... acceleration due to gravity= -9.8 m/s/s
initial velocity= 0m/s
displacement= -1.168 m
and displacement=initial velocity*time=.5*acceleration*time*time
Plug in the information we have (paying special attention to our signs), solve for time, bake until golden brown and let stand for twenty minutes...
time= .488 seconds. (No wonder it always takes me by surprise.)
Next we can find velocity right before it hits the floor, because
instantaneous velocity=initial velocity+acceleration*time
la la la
Final velocity= -4.782 m/s
So now, when my poster falls just as I'm putting the final touches on my toothpick Eiffel Tower, at least I can console myself with knowing both the time it was falling and the velocity it had before impact. Then I can go find a really big hammer.
