Royal Canin Complaint

FUNDAMENTAL PHYSICS: MATHEMATICS

Parabolic Movement

The composition of a uniform motion and a constant acceleration is a movement whose trajectory is a parabola. MRU
A constant horizontal speed vx.
A vertical MRUA initial velocity going up.
This movement is studied since antiquity. It incorporates the older books ballistics to increase accuracy in the shooting of a projectile. We call
projectile every body that once released it moves only on the acceleration of gravity.
1. Firing projectiles.
consider a cannon fires a shell from the floor (y0 = 0) with angle θ less than 90 ° to the horizontal.
The equations of motion, due to the composition of a uniform motion along the axis X, and a uniformly accelerated motion along the axis, are:
The parametric equations of the trajectory are
x = v0 · cosθ · t = v0 · senθ · t-gt2 / 2
Lost time t, we obtain the equation of
tr .1. Scope.
The horizontal span of each of the projectiles is obtained for y = 0.
Its maximum value is obtained for an angle θ = 45 °, having the same value for θ = 45 + a, that for θ = 45-a. For example, have the same range missiles fired from firing angles of 30 º and 60 º, since sin (2.30) = sin (2.60).

1.2. Maximum height.
The maximum height a projectile is obtained with v = 0.
Its maximum value is obtained for the firing angle θ = 90 °.

1.3 Abstract. Flight time

Maximum range Maximum height

.4. Tyre parabolic initial height.
It fires a projectile from a height h on a horizontal plane with initial speed v0 at an angle θ with the horizontal. To describe the motion establish a reference system as shown in Fig.
The components of the velocity of the projectile as a function of time are:
vx = v0 = v0 · · cosθvy senθ-gd t
The position of the projectile is a function of time ·
x = v0 t = cosθ · h + v0 · senθ · tg · t2 / 2
These are the parametric equations of the trajectory, and that given the time t gives the y position of the projectile.


Proceeding similarly we can derive the equations for the maximum range, maximum height and flight time.
range of a projectile to an initial velocity of 60 m / s and different angles of tiroayectoria (equation of a parabola)