Projectile Motion Calculator

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.

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.

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.