By using the same method which I've used before I've got the following equation:
t= ∫x1x2√((1+f'(x)^2)/(2g(f(x)-f(x1)))dx ,
where t is the time required to finish the whole path.
So we need the find the minimal value of this expression with x1 and x2 fix parameters, which atm i don't know how...
Guys i may have another idea to solve the problem, but in order to make sure my solution is right i need you guys to clarifai the following statements:
If an object moves in one dimension(line) and the speed of the object is given in the function of position the whole time required to the object...
Why? I have the velocitys in the function of position, so I integrated that way. Its basically continuous function which has an average value, that's what we need as i know.
Guys I have the following homework problem to solve:
There are 2 given points in a plane. If we take a point-like object with mass m and take it to the "higher" point what path should it go on to reach the other point in the shortest possible time. Only gravitational force affects our point-like...