In the movie, Apollo 13, starring Tom Hanks, scenes were filmed involving weightlessness. Weightlessness can be simulated using a plane to fly a special manoeuvre. The plane follows a specific inverted parabolic arc followed by an upward-facing recovery arc. Suppose the parabolic arc starts when the plane is at 7200 m and takes it up to 10 000 m and then back down to 7200 m again. It covers approximately 16 000 m of horizontal distance in total.
a) Determine the quadratic function that represents the shape of the parabolic path followed by the plane if the origin is at ground level directly below where the plane starts the parabolic arc.
+23254 A parabola can have this form: y - k = a(x - h)²
where (h,k) is the vertex and a is an expansion factor.
The points that you describe can be interpreted as (0, 7200), (8000, 10000) and (16000, 7200) with the vertex at (8000, 10000). I got the 8000 because it has to be halfway between the starting x-value (0) and the ending x-value (16000).
Thus, x = 8000 and y = 10000. Putting them into the equation to find the value of a:
y - 10000 = a(x - 8000)²
I can use any point for the values of x and y, so I will choose (0, 7200):
7200 - 10000 = a(0 - 8000)²
-2800 = a(64000000)
a = -2800 / 64000000 = -7/160000
So, an equation of the parabola is: y - 10000 = (-7/160000)(x - 8000)²
+130511 I answered a similar question to this earlier today.....see the solution, here...http://web2.0calc.com/questions/water-is-spraying-from-a-nozzle-in-a-fountain-forming-a-parabolic-path-as-it-travels-through-the-air-the-nozzle-is-10-cm-above-the-surface
+23254 A parabola can have this form: y - k = a(x - h)²
where (h,k) is the vertex and a is an expansion factor.
The points that you describe can be interpreted as (0, 7200), (8000, 10000) and (16000, 7200) with the vertex at (8000, 10000). I got the 8000 because it has to be halfway between the starting x-value (0) and the ending x-value (16000).
Thus, x = 8000 and y = 10000. Putting them into the equation to find the value of a:
y - 10000 = a(x - 8000)²
I can use any point for the values of x and y, so I will choose (0, 7200):
7200 - 10000 = a(0 - 8000)²
-2800 = a(64000000)
a = -2800 / 64000000 = -7/160000
So, an equation of the parabola is: y - 10000 = (-7/160000)(x - 8000)²
