# Projectile Motion Calculator

**Projectile Motion Calculator:** Have you ever watched an arrow fly through the air? I believe you did at some time and noticed that the arrow will move upwards until it reaches a certain point, then ahead, and then downward. Do you want to do some calculations with the time of flight, velocity components, the maximum height of the flight, and so on? Rather than struggling with all of the projectile motion equations, you can just use our Projectile Motion Calculator.

### What is Projectile Motion?

If a particle or object is hurled closer to the earth's surface, it will move in a curved route with continuous acceleration towards the earth's surface. The course is referred to as a trajectory of the projectile, and the motion is referred to as Projectile Motion.

### Analysis of Projectile Motion

Consider an object that is moving in a projectile motion. If the object's initial velocity is V, its initial height is h, and the angle of launch is α, you may find the remainder of the parameters, such as range, velocity components, time of flight, maximum height, and so on, as shown below.

### Calculating Velocity Components

Vx = V*cos(α) is the horizontal velocity component.

Vy = V*sin(α) is the vertical velocity component.

The right triangle is formed by the three vectors V, Vx, and Vy. A horizontal projectile motion is defined as one in which the vertical velocity component is zero. It is said to be a free fall if = 90°.

### Equation of Motion

The following are the formulas for calculating velocity, distance, and acceleration. Throwing a cricket ball, an angry bird, an arrow, or a stone in a river are all examples of projectile motion. When you release them, gravity is the only force acting on them, and it causes an equal and unbiased acceleration.

Distance Horizontal Distance x = Vx * t

- Where, t = time
- Vertical Distance from the ground y = h + Vy * t – g * t^2/2 Where, g = gravity

The velocity of Projection Formula Horizontal Velocity = Vx

Vertical Velocity = Vy -g*t

Acceleration Horizontal Acceleration = 0

Vertical Acceleration = -g because the projectile is only affected by gravity.

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### Range of Projectiles Formulae

The horizontal distance travelled by a projectile during its flight time is known as its range. The formula is R = Vx * t = Vx * 2 * Vy / g if the object is hurled from the ground. R = V^2 * sin(2α) / g is a rewriting of the formula. When the initial elevation is not zero, the formula becomes a little more difficult, and we can write it as R = Vx.

### Maximum Projectile Height Formula

If an object continues to rise after reaching its maximum height, it will eventually fall to the ground. In the instant t(Vy=0), the Vertical Velocity Component shifts from positive to negative and equals zero.

We can rewrite this equation as t(Vy=0) = Vy / g if Vy – g * t(Vy=0) = 0.

The equation for calculating the vertical distance from the ground is hmax = Vy * t(vy=0) – g * (t(Vy=0))^2 / 2 = Vy^2 / (2 * g) = V^2 * sin(α)^2 / (2 * g)

If we want to shoot a projectile at a specific height 'h' we simply add it to the applicable calculation hmax = h + V^2 * sin(α)^2/ (2 * g)

### How to use the Projectile Motion Calculator?

The process for using the projectile motion calculator is as follows

- Step 1: Fill in the appropriate input fields with the unknown velocity, initial height, angle, and x values.
- Step 2: To obtain the result, select "Calculate the Unknown" from the drop-down menu.
- Step 3: Finally, the normal force will be displayed at the range of projectile motion.

### FAQs on Projectile Motion Calculator

**1. Is it necessary for projectile motion to be horizontal?**

No, projectile motion and its equations apply to all moving objects where gravity is the only force acting on them. Objects that are thrown straight up, horizontally, with a horizontal and vertical component, and those that are just dropped fall under this category.

**2. What are the characteristics of projectile motion?**

The qualities of projectile motion include the object's horizontal velocity remaining constant, its vertical velocity changing constantly owing to gravity, the trajectory being a parabola, and the object being unaffected by air resistance.

**3. How do I calculate projectile motion acceleration?**

In projectile motion, there is only one force acting on an object: gravity. Any change in vertical speed is caused by gravitational acceleration, which on Earth is 9.81 m/s^2 (32.2 ft/s^2). Because air resistance is believed to be insignificant in the horizontal direction, there is no change in speed, hence acceleration equals 0.

**4. What factors influence the horizontal motion of a projectile?**

A projectile fired horizontally will be affected by its beginning velocity, the original height from which it is launched, and gravity. Although air resistance influences real life, it is insignificant in most theoretical calculations and is so overlooked. If the projectile has wings, it will glide, which will affect its motion.

**5. How does a projectile motion's weight impact it?**

In projectile motion, there is only one force acting on an object: gravity. Any change in vertical speed is caused by gravitational acceleration, which on Earth is 9.81 m/s^2 (32.2 ft/s^2). Because air resistance is believed to be insignificant in the horizontal direction, there is no change in speed, hence acceleration equals 0.