In a free fall ride, the object (car) is projected, at time 0, with some initial velocity. Suppose that velocity has a horizontal component of h metres per second and a vertical component of v metres per second.
It is assumed that the only force acting on this body is that of gravity. Air resistance is assumed to be insignificant. Consider the position of the car at time t seconds after "launch", measured from the launch position.
There are no forces acting on it in the horizontal direction. So, following Newton's law, it continues to travel in the horizontal direction at h metres per second. And therefore, its position is ht metres from the launch position.
In the vertical direction, the force is a downward acceleration of g metres per second2. So the vertical position at time t, is vt - 1/2*gt2.
Thus x = ht
and y = vt - 1/2*gt2
From the first equation, t = x/h. Substituting this in the second gives
y = v*x/h - 1/2*g(x/h)2 = -(1/2*g/h2)x2 + (v/h)*x
that is, y = Ax2 + Bx for some constants A and B
[specifically A = -(1/2*g/h2), and B = (v/h), but the exact values are not relevant here.]
Now y = Ax2 + Bx is the quadratic function model, therefore it is a suitable model for such motion.
Chat with our AI personalities
A real life example of the sine function could be a ferris wheel. People board the ride at the ground (sinusoidal axis) and the highest and lowest heights you reach on the ride would be the amplitudes of the graph.
ride in a plane. you would fly a plane
the quadratic formula is really complex. so, if you can avoid it, you should. one way i do this is by getting the trinomial into X^2 - 2YX + Y^2 = 0 form. here's an example lets say we have x^2 - 2x - 5 = 0 normally we would have to do the quadratic formula however, if we get it into this form, we can get x^2 - 2(1)x + 1 = 6 all i did was add 6 to both sides of the equation. you can now simplify the left side of the equation, and be left with (x-1)^(2) = 6 to get ride of the exponent on the left side, find the square root of both sides. this will leave you with (x-1) = (+ or -)radical(6) add one to both sides and you will get x = 1 (+ or -)radical(6) therefore, x can equal 1 + radical(6) or 1 - radical(6) now, this may seem complex, but it is easy once you get used to it. It is far more efficient than the long quadratic formula.
Rode
1