Bottom Sling
Bottom Sling
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Pentunia Pickle Bottom Sojourn Sling Video Tuturial
Frequently Asked Questions:
Shoveling Dirt Derivative Problem?
You sling a shovelful of dirt up from the bottom of a 17 ft hole with an initial velocity of 32 ft/s. Is that enough speed to get the dirt out of the hole, or had you better duck?
The answer is "no", but I don't know why... Please explain thoroughly step by step. Thanks!
The derivative of your velocity would be -32 ft/s^2, which would be your a(t).
Doing the antiderivative, you get v(t) = -32t + C
Since v(0) = 32, C = 32.
v(t) = -32t + 32
Doing the antiderivative once more, you get s(t) = -16t^2 + 32t + C
Since s(0) = -17, C = -17
s(t) = -16t^2 + 32t - 17
By graphing v(t) and finding its vertex (the maximum height), which is v(0), you find that this occurs at t = 1.
Plug this into s(t):
s(1) = -1
Therefore, the dirt is at -1 ft at it's maximum height, below ground level.
This means that you should duck.
Hope this helps! Rate as best answer, please 
Bottom Sling
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