# Projectile Motion Calculator

Projectile Motion Calculator is a free tool that analyzes the motion of an object projected into the air parobolically. Make all your calculations regarding projectile motion in a matter of seconds taking help of the free online tool.

### What is meant by Projectile Motion?

If a particle or object is thrown nearer to the earth's surface, the object would move towards the earth's surface along a curved path with constant acceleration. Such path is known as trajectory or projectile and the motion is known as Projectile Motion.

Examples of Projectile Motion include throwing a cricket ball, angry bird, arrow, or stone in a river, etc. The moment you release them the only force acting on them is gravity and it creates an equal impartial acceleration.

### Projectile Motion Analysis

Let us consider an object is having projectle motion. If the initial velocity of the object is V, initial height is h, angle of launch is α you can find the rest of the parameters like range, components of velocity, time of flight, maximum height, etc. as described below.

**Calculating Components of Velocity**

Horizontal Velocity Component is given by Vx = V*cos(α)

Vertical Velocity Component is given by Vy = V*sin(α)

All the three vectors V, Vx, Vy form a right traingle.

If the vertical velocity component is 0 then it is said to be a horizontal projectile motion. If α = 90° then it is said to be a free fall.

**Equations of Motion**

Formulas to calculate the velocity, distance and acceleration are as follows

**Distance**

Horizontal Distance x = Vx * t in which t is the time.

Vertical Distance from the ground is given by y = h + Vy * t – g * t2/2 in which g is the gravity

**Velocity of Projection Formula**

Horizontal Velocity = Vx

Vertical Velocity = Vy -g*t

**Acceleration**

Horizontal Acceleration = 0

Vertical Acceleration = -g since only gravity acts on the projectile

**Range of Projectile Formula**

Range of a Projectile is nothing but the horizontal distance covered during the flight time. If the object is thrown from the ground then the formula is R = Vx * t = Vx * 2 * Vy / g. We can rewrite the formula as R = V2 * sin(2α) / g

In case of intial eleveation not being zero the formula gets a bit complicated and we can write it as R = Vx

**Maximum Height of Projectile Formula**

If an object moves upwards after reaching the maximum height it keeps falling towards the earth. Vertical Velocity Component changes from positive to negative and is equal to zero in a moment t(Vy=0).

If Vy – g * t(Vy=0) = 0 then we can reframe this equation as t(Vy=0) = Vy / g

Finding the vertical distance from ground we have the equation as hmax = Vy * t(vy=0) – g * (t(Vy=0))² / 2 = Vy2 / (2 * g) = V2 * sin(α)2 / (2 * g)

If we throw a projectile at a certain height 'h' we simply have to add that in the relevant formula hmax = h + V2 * sin(α)² / (2 * g)

Physicscalc.Com has got concepts like friction, acceleration due to gravity, water pressure, gravity, and many more along with their relevant calculators all one under one roof.

### FAQs on Projectile Motion Calculator

**1. What factors affect projectile motion?**

Three major factors that affect the projectile motion are projection angle, magintude of projection velocity, height of projection.

**2. What is the formula for Maximum Height in Projectile Motion?**

Formula for Maximum Height in Projectile Motion is hmax = h + V² * sin(α)² / (2 * g)

**3. Does weight affect a Projectile Motion?**

Yes, greater the weight of an object the greater the gravity influence on it in case of a Projectile Motion. Gravity stops the upward movement thus pulling the object downwards, thus limits the vertical component of projectile.

**4. What is acceleration at a Maximum Height?**

At a Projectile's maximum height the acceleration is zero.