# Projectile formula question

i found these 2 formulas on a web site and it says these are projectile motion formulas both horizontal motion and vertical motion.

HORIZONTAL MOTION
x2 = x1 + Vx1t

VERTICAL MOTION
Y2 = Y1+ Vy1t - 0.5gt2

in terms of physics do these formulas work out things that are fired from e.g. a gun etc.? i was thinking that are these formulas to work out the angle and velocity of the moving object?

any help would be apprecated

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#### enigma

Staff Emeritus
Gold Member
These are the formulas to determine position (x2,y2) as a function of initial position (x1,y1), initial velocity (Vx,Vy), time (t), and gravity (g).

The angle the thing is launched at is just atan(Vy/Vx).

#### arcnets

Yes they do. But only if you neglect for friction.
As for velocity:
Velocity in x: Vx = dX2/dt
Velocity in y: Vy = dY2/dt
Absolute velocity: V = sqrt(Vx^2 + Vy^2)
As for angle (WRT x-axis):
tan (alpha) = Vy/Vx.

#### Will

Whoa arcnets!! Going differential equations style! Slick Maybe I might understand the calculus of kinematics better after this semester.Anyway:

The horizontal component of the projectile is constant in this idealized situation. The vertical component changes due the acceleration of gravity, and its horizontal position is exactly analogous to an object thrown directly up at with velocity Vy1 from an initial height y1. Like arcnets said ,the total initial V is (Vx^2+Vy^2)^.5 and theta initial equals arctan(Vy1/Vy2x).Think of the components forming the two perpendicular sides of a right triangle with hypotenuse V total making angle theta with the horizontal. A convenient way of expressing these two equations and the ones you provided:

HORIZONTAL MOTION
x2 = x1 + Vx1t = x(t) =x1 + cos(theta)+Vx1t

and

VERTICAL MOTION
Y2 = Y1+ Vy1t - 0.5gt2 = y(t) =y1 +sinVy1 - 0.5gt^2

These idealized equations are the foundation, but in practical applications such as missle deployment, factors such as wind, air density, temperature are to greate to be ignored.

#### Alexander

All projectile equations are derived from fact that projectile is in free fall, so its acceleration is always a=g.

Integrate this equation over time once: v(t)=gt+v0, twice: r(t)=gt^2/2+v0t+r0

Projecting vectors in xyz directions yeilds all projectile equations in component form.