I was a driving instructor for Porsche and BMW car clubs for 12 years. My track car was an older turbocharged Porsche. Most of my events were at Road Atlanta, a fast track where one is mostly at full throttle or threshold braking. I drove my track car to the events. The distance was 236...
But why do physical systems seek the minimum? The ball near the bottom of a valley finds its resting place at the bottom which, coincidentally, is the point of minimum PE.
Many, many years ago while in engineering graduate school I was studying calculus of variations. One classic problem was to determine the shape of a hanging cable supported at its two ends. After minimizing the integral, the catenary curve was the solution. The basic assumption in setting up...
Due to its nonlinearity you'll have to perform a numerical integration in order to solve it. Newton Raphson embedded in a fully implicit scheme would work well.
"find the ratio of the effective cross-sectional area A in the slower position to that in the faster position."
Should the ratio be greater than or less than unity?
I get close to your answers because one should round off after the computation is completed. Don't round off your time, then use the rounded time to compute other results.
You are attempting to subtract meters/second from meters. You cannot do that.
What about the formula
y = Vo*t + .5*a*t^2
where Vo is initial VERTICAL velocity
a is acceleration of gravity
t is time
y is distance of free fall
No, the 250 m/s is the horizontal velocity and is extraneous data. The problem is the same as if you dropped a brick off a 45 m high building. How long would it take to reach the ground?
That is correct. Therefore you have a free fall problem. The muzzle velocity is analogous to the moving airplane. It is extraneous data that is supplied to confuse the student.
Hint: When the U tube balances out, the pressure at the lowest point of bend due to the left column of Hg must equal the pressure due to the right column of Hg plus H2O. Pressure is density times depth.