Our projectile motion calculator is a tool that helps you analyze the parabolic projectile motion. It can find the time of flight, but also the components of velocity, the range of the projectile, and the maximum height of flight. Continue reading if you want to understand what is projectile motion, get familiar with the projectile motion definition, and determine the abovementioned values using the projectile motion equations. Prefer watching over reading? Learn all you need in 90 seconds with this video we made for you:
Imagine an archer sending an arrow in the air. It starts moving up and forward, at some inclination to the ground. The further it flies, the slower its ascent is – and finally, it starts descending, moving now downwards and forwards and finally hitting the ground again. If you could trace its path, it would be a curve called a trajectory in the shape of a parabola. Any object moving in such a way is in projectile motion. Only one force acts on a projectile – the gravity force. Air resistance is always omitted. If you drew a free body diagram of such an object, you would only have to draw one downward vector and denote it “gravity”. If there were any other forces acting on the body, then – by projectile motion definition – it wouldn't be a projectile.
Projectile motion is pretty logical. Let's assume you know the initial velocity of the object V, the angle of launch α, and initial height h. Our projectile motion calculator follows these steps to find all remaining parameters:
If the vertical velocity component is equal to 0, then it's the case of horizontal projectile motion. If, additionally, α = 90° then it's the case of free fall.
Distance
Velocity
Acceleration
hmax = h + V² * sin(α)² / (2 * g)
Uff, that was a lot of calculations! Let's sum that up to form the most essential projectile motion equations:
Using our projectile motion calculator will surely save you a lot of time. It can also work 'in reverse'. For example, enter the time of flight, distance, and initial height and watch it do all calculations for you!
No, projectile motion and its equations cover all objects in motion where the only force acting on them is gravity. This includes objects that are thrown straight up, those thrown horizontally, those that have a horizontal and vertical component, and those that are simply dropped.
Objects with projectile motion include: keys being thrown, a 300 kg projectile being thrown 90 m by a trebuchet, a football being kicked so that it no longer touches the ground, a diver jumping from a diving board, an artillery shell the moment it leaves the barrel, and a car trying to jump a bridge.
There is only one force acting on a projectile - gravity. This means that an object will eventually fall to Earth. But what about if the object is moving so fast horizontally that, by the time it reaches the ground, the ground is no longer there? This is the principle that governs satellites.
There is only one force acting on an object in projectile motion - gravity. This means that any change in vertical speed is due to gravitational acceleration, which is 9.81 m/s2 (32.2 ft/s2) on Earth. In the horizontal direction, there is no change in speed, as air resistance is assumed to be negligible, so acceleration is 0.
Initial velocity, the initial height the projectile is being launched from, and gravity will all affect a projectile launched horizontally. Air resistance will also have an effect in real life, but for most theoretical calculations it is negligible and is therefore ignored. If the projectile has wings, this will also impact its motion, as it will glide.
A projectile is an object that is in motion, in the air and has no force acting upon it other than the acceleration due to gravity (this means that it cannot be self-propelled). You can probably think of many examples: a thrown ball or a stone thrown from a trebuchet. Even the Moon is a projectile, with respect to the Earth!
The properties of projectile motion are that the object’s horizontal velocity does not change, that it’s vertical velocity constantly changes due to gravity, that the shape of its trajectory will be a parabola, and that the object is not affected by air resistance.
Galileo was the first person to describe projectile motion accurately, by breaking down motion into a horizontal and vertical component, and realizing that the plot of any object's motion would always be a parabola. He described it in his book, On Motion, published around the 1590s.
An object follows a parabola because of how its two components of motion - the horizontal and vertical - are affected by gravity. The horizontal component is not affected by gravity at all, and so changes in a constant, linear fashion. The vertical part, however, is constantly affected by gravity, and so it will increase in height, and then decrease, accelerating due to gravity.
The equation for the distance traveled by a projectile being affected by gravity is sin(2θ)v2/g, where θ is the angle, v is the initial velocity and g is acceleration due to gravity. Assuming that v2/g is constant, the greatest distance will be when sin(2θ) is at its maximum, which is when 2θ = 90 degrees. This means θ = 45 degrees. |