Physics Calculators ▶ Projectile Motion Calculator

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An online projectile motion calculator computes the velocity, height, and flight duration at a given time. This Projectile calculator analyzes the parabolic motion and solves a special case where an object is launched from an elevated plane horizontally. Continue reading to learn projectile motion with different equations and much more.

In physics, a projectile motion is defined as the motion of an object thrown into the air and subjected to gravitational acceleration. The path followed by the object is called the trajectory, while an object is indicted as the projectile, and the movement of the object is called the motion of the projectile.

The projectile motion of the object can be in any form, such as straight path, circular trajectory, parabola, hyperbola, ellipse, etc. The projectile motion equations are used in engineering structures. The motion of the projectile provides a clear idea of â€‹â€‹the motion of an object that is close to the earth’s surface and accelerated by the gravity near the surface of the earth.

**The most essential projectile motion equations are:**

Projecting an object from the earth surface, where initial height h = 0

Horizontal velocity component: V_x = cos(Î±) * V

Vertical velocity component: V_y = sin(Î±) * V

Flight duration: t = V_y / g * 2

Range of the projectile: R = V_y / g * V_x * 2

Maximum height: maxh = V_y^2 / (2 * g)

**Projecting the object from some height where initial height h > 0**

Horizontal velocity component: V_x = cos(Î±) * V

Vertical velocity component: V_y = sin(Î±) * V

Time of flight: t = [\sqrt{(Vy^2 + 2 * g * h)} + V_y] / g

Range of the projectile: R = V_x * [\sqrt{(V_y^2 + 2 * g * h)} + V_y] / g

Maximum height: hmax = V_y^2 + h/ (2 * g)

Using our projectile motion calculator with initial height will surely save your time and precisely provide the required values.

The key components that we need to keep in mind when solving the physics projectile motion problems:

Î˜ = Initial launch angle,

u = Initial velocity

T = Time of flight

A = Acceleration

V_x = Horizontal velocity

V_y = Vertical velocity

d = Displacement

H = Maximum height

R = Range

Here are some equations that the projectile motion calculator uses:

- The horizontal distance can be represented as x = t * Vx, where time is t.
- A projectile calculator finds the vertical distance from the surface of the earth with the equation

y = h + t * V_y â€“ g * t_2 / 2

Where the gravity acceleration is represented by g and vertical velocity with v_y.

The horizontal velocity is equal to V_x, and vertical velocity can be expressed as t * V_y â€“ g.

Horizontal acceleration is equal to zero, and vertical acceleration is equal to -g (because only gravity acts on the projectile).

The flight ends when the projectile object hits the surface of the earth. It happens when the vertical distance from the surface is 0. In the case where the initial height (h) is 0, the formula can be written as: Vy * t â€“ g * tÂ² / 2 = 0.

So, the equation used by maximum height calculator to find that the duration of flight is:

t = 2 * Vy / g =2 * V * sin(Î±) / g.

However, if we’re projecting an object from some height, then the equation is not working so nicely as earlier. So, we get a quadratic equation to evaluate:

h + V_y * t â€“ g * t_2 / 2 = 0

After simplifying this equation, we get:

t = [V * sin(Î±) + \sqrt {((V * sin(Î±))_2 + 2 * g * h)} ] / g

The range of the projectile is calculated by the projectile motion solver, where the total horizontal distance is the distance traveled during the flight time. Again, if we’re throwing the object from the surface where the initial height is zero, then we can write the formula as:

R = t * V_x = V_y * 2 * V_x / g

It may changed into the form of:

R = sin(2Î±) * V_2 / g

When an object reaches the maximum height, it stops moving upward and begins falling. It means that the vertical velocity changes from positive to negative.

If V_y â€“ g * t (v_y = 0) = 0, then we can transformed this equation to:

t (V_y=0) = V_y / g

Now, find the vertical distance from the surface at that time:

= V_y * t(v_y = 0) â€“ g * (t(V_y = 0))^2 / 2

= V_y^2 / (2 * g) = sin(Î±)^2 * V^2 / (2 * g)

When launching an object from some initial height h, we need to substitute that value into the formula:

= h + V^2 * sin(Î±)^2 / (2 * g)

An online projectile calculator defines the motion of an object that is projected into the air. These are the few simple steps that you need to look for in order to find projectile motion:

- Firstly, choose an option from the drop-down list, which you need to calculate the projectile motion with that particular parameter.
- Now, substitute the values according to the selected option.
- Click on the “Calculate” button to determine the projectile.

**The Calculator calculates:**

- Initial Horizontal Velocity (Vx)
- Initial Vertical Velocity (Vy)
- Gravitational Acceleration

If you select the flight parameters at a given time from the drop-down list, then it’ll provide:

- Horizontal Position
- Height

The projectile follows a parabola because gravity affects the two components of horizontal and vertical motion. The horizontal component is not affected by gravity. However, the vertical part is constantly affected by gravity, so its height increases first, then decreases and accelerates under the influence of gravity.

The initial height, the projectile’s initial velocity, and the gravitational force is acting on the horizontal projectile. Air resistance also impacts real life, but it can be ignored for most theoretical calculations. If the object has wings, this will also affect its movement when gliding.

The characteristic of projectile motion is:

- The horizontal speed of the object is constant.
- The vertical speed is constantly Changes due to gravity.
- The trajectory shape is a parabola, and the object is not affected by the air resistance.

Use this online projectile motion calculator to analyze the parabolic movement of projectiles. It can determine the range, components of velocity, height, flight parameters at a given time in a fraction of a second.

From the source of Wikipedia: Kinematic quantities of projectile motion, Trajectory of a projectile with air resistance, Trajectory of a projectile with Stokes drag, Trajectory of a projectile with Newton drag, Lofted trajectory.

From the source of lumen physics: Horizontal Motion, Vertical Motion, Vector Addition, and Subtraction: Analytical Methods, Total displacement, and velocity.

From the source of Saratoga Springs: Projectile Motion and Inertia, Newton’s law of inertia, Describing Projectiles With Numbers, Horizontal and Vertical Velocity.