Here's a physics problem?

Question

A person jumps off a 45-m building. He goes to the top of the building and jumps in the parabola f(x) = 6x -x^2 where x is the

number of metres above the building's height. Calculate the

person's gravitational potential energy at the maximum height

relative to the ground. (hint: find the max. height then add 45)

Answer 1

Max height is 48 meters. So max gravitational potential is PE=mgh where g is gravity m is the persons mass and h is the max height, this case 48 meters.

Answer 2

first we know that the person when jumping executes a parabolic trajectory.no person can ever jump down straight from a building.now the person does go up to some height as soon as he jumps off and then starts to fall down in a straight line as soon as he is back to the same point from where he started to jump.after this point he begins to fall down in a straight line due to acceleration due to gravity.

therefore the net displacement of the person is the height of the building,as displacement while covering the parabolic path is zero as the person is back to where he started from.therefore we can equate the displacement equation to zero and solve for x.therefore we get x=0(not possible) and x=6m, but x=6m represents twice the displacement and therefore 2x=6m. hence x= 3m. you can also get the same by differentiating the displacement equation 6x-x^2 and getting 6-2x, which on setting equal to 0 for maxima or minima gives x=3. On further differentiation, we get -2 <0 and hence x=3 is max heigh abpve surface of the building.

therefore the maximum height that the person can reach above the ground while jumping is 45m+3m=48m.

therefore the person's gravitational potential energy at that height is mass of the person*9.81m/s^2(accn.due to gravity)*48m.