1) We have a problem dealing with acceleration in terms of velocity (weird, I know, but it's what it is). Here's the skinny:
a = -2v ft/s<sup>2</sup>
x<sub>0</sub> = 2 ft
v<sub>0</sub> = 10 ft/s
My book shows you solving this by using dx = v*dv/a to get x, so I got for the distance the particle falls before stopping, 22ft.
It also shows using dt = dv/a to get t, which unfortunately ends up as -.5 ln(v/vo), and while solving to find the time at which v = 1 ft/s, it works fine and I get something like 1.15s, but for v=0, well, it's a natural log, and natural log of zero is [lol].
2) We have a problem with a pressure cooker, which I think is retarded to begin with. It says the pressure outside the cooker (the atmosphere) is 101KPa. The pressure inside the cooker (gage pressure) is 100KPa. This makes a net pressure difference of 1KPa, right? Idk.
You have a little piece of metal that the pressure on the inside will force up if the pressure gets too high, and the idea is to find the mass. The metal is 4mm<sup>2</sup> in area.
I did the sum of the forces = 0, which is the net pressure times the area plus the mass of the metal times gravity, and infuriatingly, my answer was off by a [couple] order[s] of magnitude. Instead of 40.8g, mine had a mass of .4077g.