Projectile formula question

In summary, the formulas x2 = x1 + Vx1t and Y2 = Y1+ Vy1t - 0.5gt2 are used to determine position and velocity of a projectile in both horizontal and vertical motion. These equations are derived from the concept of free fall and take into account factors such as initial position, velocity, time, and gravity. They can be used to calculate the angle and velocity of a moving object, such as a projectile fired from a gun. However, in practical applications, other factors such as wind and air density may need to be considered.
  • #1

Radiatedtheory18

i found these 2 formulas on a website 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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  • #2
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).
 
  • #3
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.
 
  • #4
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.


 
  • #5
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.
 

What is the projectile formula?

The projectile formula calculates the vertical and horizontal displacement of an object in motion, taking into account the initial velocity, angle of launch, and gravitational force.

How do you calculate the initial velocity in the projectile formula?

The initial velocity can be calculated by dividing the horizontal displacement by the time it takes for the object to reach its peak height. Alternatively, it can also be calculated using the horizontal and vertical velocities at a specific point in time using trigonometric functions.

What is the significance of the angle of launch in the projectile formula?

The angle of launch determines the initial direction of the object's motion and affects the range and maximum height of the projectile. A higher angle will result in a longer range but a lower maximum height, while a lower angle will result in a shorter range but a higher maximum height.

How does air resistance affect the projectile formula?

Air resistance can cause the projectile to lose speed and change its trajectory, making it more difficult to predict its motion. It is often neglected in simple projectile formulas, but can be taken into account in more complex equations.

What are some real-world applications of the projectile formula?

The projectile formula is used in a variety of fields, including physics, engineering, and ballistics. It can be used to predict the motion of projectiles such as bullets, artillery shells, and rockets, as well as in sports like basketball, baseball, and golf. It is also used in the design and testing of structures like bridges and buildings.

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